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Proceed to Safety

# Minimally Complex Sequences

5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, 5, -5, ...

MCS62215 : A0 = 5; AN = - AN-1 (score: 5)

MCS26744374 : A0 = 1; A1 = 1; A2 = 1; AN = - 2 AN-3 - 1 (score: 5)

MCS13816582 : A0 = 1; A1 = 1; AK+1 = - 2 AK - AK-1 + K (score: 5)

MCS877249 (alias MCS3508997, MCS3508998, MCS7017997)

A0 = 0; A1 = 0; AN = - 2 AN-2 - 1 (score: 4)

MCS3461174 : A0 = 1; A1 = 1; AK+1 = - AK - K AK-1 + K (score: 5)

MCS1002320 : A0 = 1; AK+1 = - 2 AK + 2 K + 1 (score: 5)

MCS109633 (alias MCS3508278) : A0 = 0; A1 = 1; AK+1 = - K AK-1 + AK-1 - 1 (score: 5)

Example of a simple recurrence not in OEIS

MCS7878 (alias MCS126056) : A0 = 0; AK+1 = - K AK + K2 - 1 (score: 5)

MCS1597793 : A0 = 0; A1 = 0; A2 = 1; AK+1 = - 2 AK-2 - K (score: 5)

MCS505544 : A0 = 1; AK+1 = - AK + K2 - K - 1 (score: 5)

MCS1581409 : A0 = 0; A1 = 0; A2 = 1; AN = AN-2 - 2 AN-3 (score: 5)

MCS27445 (alias MCS1717633) : A0 = 0; A1 = 1; AK+1 = - 2 AK-1 - K - 1 (score: 5)

MCS3347 : A0 = 0; A1 = 1; AK+1 = 3 AK-1 + K (score: 5)

MCS124296 : A0 = 1; AK+1 = - 2 AK + K2 (score: 4)

MCS868873 : A0 = 0; A1 = 0; AK+1 = K AK-1 + AK-1 + 1 (score: 5)

MCS434193 : A0 = -1; A1 = 0; AK+1 = K AK-1 + 1 (score: 5)

MCS6725 (alias MCS792753, MCS3443462) : A0 = 0; A1 = 1; AN = AN-1 - 2 AN-2 (score: 4)

Lucas and Lehmer numbers with parameters (1+-sqrt(-7))/2 (A107920)

Horadam sequence Wn(0, 1; -2, 1), Lucas sequence Un(1, 2) ; Horadam sequence Wn(1, 1; -2, 1)

MCS3459846 (alias MCS3459845) : A0 = 1; A1 = 1; AN = - AN-1 - 2 AN-2 (score: 4)

Horadam sequence Wn(1, 1; -2, -1) ; Horadam sequence Wn(0, -1; -2, -1)

MCS26871350 : A0 = 1; A1 = 1; A2 = 1; AN = AN-1 - AN-3 - 1 (score: 5)

MCS3453702 : A0 = 1; A1 = 1; AN = - 2 AN-1 - AN-2 (score: 4)

Horadam sequence Wn(1, 1; -1, -2)

MCS12747830 : A0 = 1; A1 = 1; A2 = 1; AK+1 = AK-2 + 2 K (score: 5)

MCS26936886 : A0 = 1; A1 = 1; A2 = 1; AN = - AN-1 - AN-3 - 1 (score: 5)

MCS124616 (alias MCS249105) : A0 = 1; AK+1 = - AK + K2 - K (score: 4)

MCS1622369 : A0 = 0; A1 = 0; A2 = 1; AN = - AN-1 - 2 AN-3 (score: 5)

MCS3510326 : A0 = 1; A1 = 1; AK+1 = - K AK-1 + K - 1 (score: 5)

MCS53536 : A0 = 0; A1 = 1; AK+1 = K AK-1 + AK-1 + K (score: 5)

MCS54274 : A0 = 0; A1 = 1; AK+1 = 2 K AK-1 + 1 (score: 5)

MCS876589 : A0 = 0; A1 = 0; AK+1 = - 2 K AK-1 - 1 (score: 5)

MCS855173 : A0 = 0; A1 = -1; AK+1 = - AK-1 + K2 (score: 5)

MCS124320 (alias MCS1010497) : A0 = 1; AK+1 = - 2 AK + K (score: 3)

MCS13492 : A0 = 0; A1 = 1; AK+1 = - 2 AK + AK-1 + K (score: 5)

MCS13855494 : A0 = 1; A1 = 1; AK+1 = - AK - 2 AK-1 - K (score: 5)

MCS25347638 : A0 = 1; A1 = 1; A2 = 1; AN = - 2 AN-2 - AN-3 (score: 5)

MCS13818630 : A0 = 1; A1 = 1; AK+1 = - 2 AK - AK-1 - K (score: 5)

MCS14155 (alias MCS251712) : AK = 4 K + 1 (score: 5)

MCS808993 : A0 = 0; A1 = 1; A2 = 1; AN = - 2 AN-1 + AN-3 (score: 5)

MCS25986614 : A0 = 1; A1 = 1; A2 = 1; AN = - AN-1 + AN-2 - AN-3 (score: 5)

MCS13515 : A0 = 0; A1 = 1; AN = - AN-1 + 4 AN-2 (score: 6)

(Not in OEIS)

Horadam sequence Wn(0, 1; 4, -1), Lucas sequence Un(-1, -4)

MCS13451 : A0 = 0; A1 = 1; AN = AN-1 + 4 AN-2 (score: 6)

Horadam sequence Wn(0, 1; 4, 1), Lucas sequence Un(1, -4)

MCS6296374 : A0 = 1; A1 = 1; A2 = 1; AK+1 = - K AK-1 + AK-2 (score: 5)

MCS7782 : A0 = 0; AK+1 = - K AK - AK + K2 (score: 5)

MCS1767 : AK = 5 K (score: 5)

MCS1015072 : A0 = 1; AK+1 = AK + K - 3 (score: 5)

MCS6300726 : A0 = 1; A1 = 1; A2 = 1; AK+1 = AK-2 + K2 (score: 5)

MCS31154 : A0 = 0; AK+1 = - AK + 2 K2 - K (score: 5)

MCS3336 : A0 = 0; A1 = 1; AK+1 = AK-1 + K2 (score: 4)

MCS3427462 : A0 = 1; A1 = 1; AK+1 = - AK-1 + K2 + K (score: 5)

MCS7092 (alias MCS7094, MCS14158, MCS124065, MCS1006160)

AK = K2 + K - 1 (score: 4)

Same as Fibonacci polynomial N2-N-1 (A28387)

MCS1973 (alias MCS126304, MCS252609, MCS1729797)

A0 = 0; AN = - 2 AN-1 - 1 (score: 3)

Horadam sequence Wn(0, -1; 2, -1)

MCS25888310 : A0 = 1; A1 = 1; A2 = 1; AN = - 2 AN-1 - AN-3 (score: 5)

MCS876598 : A0 = 1; A1 = 1; AK+1 = - K AK-1 - 1 (score: 4)

MCS3476534 : A0 = 1; A1 = 1; AK+1 = - K AK-1 - AK-1 + 1 (score: 5)

MCS27137 : A0 = 0; A1 = 1; AK+1 = - K AK-1 + 1 (score: 4)

MCS868877 : A0 = 0; A1 = 0; AK+1 = - K AK-1 + AK-1 + 1 (score: 5)

MCS54018 : A0 = 0; A1 = 1; AK+1 = - AK + 2 K AK-1 (score: 5)

MCS53762 : A0 = 0; A1 = 1; AK+1 = AK + 2 K AK-1 (score: 5)

MCS7827 : A0 = 0; AK+1 = AK + 3 K + 1 (score: 5)

MCS3372 (alias MCS13813782) : A0 = 0; A1 = 1; AN = - 2 AN-1 + AN-2 (score: 4)

Pell numbers with signs (A77985)

Horadam sequence Wn(0, 1; 1, -2), Lucas sequence Un(-2, -1) ; Horadam sequence Wn(1, 0; 1, -2)

MCS860961 : A0 = 0; A1 = 0; AK+1 = AK - AK-1 + K2 (score: 5)

MCS248176 : A0 = 1; AK+1 = AK + 4 K (score: 5)

Centered square numbers 2N(N+1)+1 or N2+(N+1)2 (A1844)

MCS126624 : A0 = 1; AN = 2 AN-1 + 3 (score: 5)

MCS502752 : A0 = 1; AN = - 3 AN-1 + 2 (score: 5)

MCS1010529 (alias MCS2012592) : A0 = -1; AK+1 = - 2 AK - K - 1 (score: 5)

MCS28378 : AK = 2 K2 - K - 1 (score: 5)

MCS1936 : A0 = 0; AK+1 = AK + K2 (score: 3)

Square Pyramidal numbers (A0330)

MCS861709 : A0 = 0; A1 = 0; AK+1 = AK - K AK-1 - K (score: 5)

MCS3512374 : A0 = 1; A1 = 1; AK+1 = - K AK-1 - K - 1 (score: 5)

MCS26973 : A0 = 0; A1 = 1; AK+1 = 2 AK - AK-1 + 3 K (score: 7)

Magic numbers of magic squares N(N2+1)/2 (A6003)

MCS860705 : A0 = 0; A1 = 0; AK+1 = AK + AK-1 + K2 (score: 5)

MCS15658 : A0 = 0; AK+1 = 2 AK + 2 K + 1 (score: 5)

MCS6513037 : A0 = 0; A1 = 0; A2 = 0; AK+1 = - AK - AK-2 - K (score: 5)

MCS13494 : A0 = 0; A1 = 1; AK+1 = - 2 AK + AK-1 - K (score: 5)

MCS31560 (alias MCS505032) : A0 = 0; AK+1 = AK + K2 + K - 1 (score: 5)

MCS2004656 : A0 = 1; AK+1 = - 2 AK - 2 K + 1 (score: 5)

MCS125664 : A0 = 1; AN = 3 AN-1 + 2 (score: 5)

MCS249137 : A0 = -1; AK+1 = - K AK - AK + K (score: 5)

MCS7881 (alias MCS126104, MCS252209) : A0 = 0; AK+1 = - K AK + K - 1 (score: 4)

MCS974 (alias MCS3918) : A0 = 0; AK+1 = 3 AK + K (score: 4)

MCS13517 : A0 = 0; A1 = 1; AK+1 = - K AK - AK - AK-1 (score: 5)

MCS427713 : A0 = -1; A1 = 0; AK+1 = - K AK - AK-1 (score: 5)

MCS124612 : A0 = 1; AK+1 = - AK + K3 - K (score: 5)

MCS7780 (alias MCS124488) : A0 = 0; AK+1 = K AK - AK + K2 (score: 5)

MCS868961 : A0 = 0; A1 = 0; AK+1 = - K AK + AK-1 + 1 (score: 5)

MCS3416246 : A0 = 1; A1 = 1; AK+1 = - 2 K AK-1 + AK-1 (score: 5)

MCS3915 (alias MCS250592) : A0 = 0; AN = 4 AN-1 + 1 (score: 5)

(4N-1)/3 (A2450)

MCS197425 : A0 = 0; A1 = 1; A2 = 1; AK+1 = - K AK - AK-2 (score: 5)

MCS497368 : A0 = 1; AK+1 = - K AK - 2 AK - K (score: 5)

MCS31341 : A0 = 0; AK+1 = - K AK - AK - K + 1 (score: 5)

MCS14188 : AK = K3 - K - 1 (score: 5)

MCS3876 : A0 = 0; AK+1 = K AK + AK + K (score: 4)

MCS13553 : A0 = 0; A1 = 1; AN = 5 AN-1 - AN-2 (score: 7)

Horadam sequence Wn(0, 1; -1, 5), Lucas sequence Un(5, 1)

MCS62400 : A0 = 1; AN = 5 AN-1 (score: 5)

Powers of 5 (A0351)

MCS124177 : A0 = -1; AK+1 = 2 AK + K2 (score: 5)

MCS6776 : A0 = 0; A1 = 1; AN = 5 AN-1 + AN-2 (score: 7)

Horadam sequence Wn(0, 1; 1, 5), Lucas sequence Un(5, -1)

MCS505432 : A0 = 1; AK+1 = - 2 K AK - AK - 1 (score: 5)

MCS15570 : A0 = 0; AK+1 = 2 K AK - AK + K (score: 5)

MCS13882118 : A0 = 1; A1 = 1; AN = 6 AN-1 - AN-2 (score: 8)

2X2-1 is a square (A1653)

MCS7813 (alias MCS125016, MCS250033) : A0 = 0; AK+1 = - 2 K AK + 1 (score: 4)

MCS3417478 : A0 = 1; A1 = 1; AK+1 = - 2 K AK + AK-1 (score: 5)

MCS26903 : A0 = 0; A1 = 1; AN = AN-1 - 4 AN-2 (score: 6)

Horadam sequence Wn(0, 1; -4, 1), Lucas sequence Un(1, 4)

MCS62641 : A0 = 0; AK+1 = - 2 AK - K2 + 1 (score: 5)

MCS107713 : A0 = 0; A1 = 1; AK+1 = AK - K AK-1 - K (score: 5)

MCS213197 : A0 = 0; A1 = 0; AK+1 = - K AK-1 - K2 (score: 5)

MCS109573 : A0 = 0; A1 = 1; AK+1 = - 2 K AK-1 - 1 (score: 5)

MCS15629 (alias MCS125036) : A0 = 0; AK+1 = - K AK - K2 + 1 (score: 5)

MCS6686 : A0 = 0; A1 = 1; AN = 6 AN-2 (score: 7)

Horadam sequence Wn(0, 1; 6, 0), Lucas sequence Un(0, -6)

MCS13315 : A0 = 0; A1 = 1; AK+1 = 3 K AK-1 (score: 5)

MCS15608 : A0 = 0; AK+1 = - 3 AK + K2 (score: 5)

MCS109953 : A0 = 0; A1 = 1; AK+1 = - AK - K AK-1 - 1 (score: 5)

MCS13814534 : A0 = 1; A1 = 1; AN = - 2 AN-1 - 2 AN-2 (score: 5)

Horadam sequence Wn(1, 1; -2, -2)

MCS248596 : A0 = 1; AK+1 = - 2 AK + 2 K2 (score: 5)

MCS856101 : A0 = 0; A1 = -1; AK+1 = K AK-1 + K (score: 5)

MCS108129 : A0 = 0; A1 = 1; AK+1 = - AK - K AK-1 - AK-1 (score: 5)

MCS432153 : A0 = -1; A1 = 0; AK+1 = - AK - K AK-1 (score: 5)

Quick Index:

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