cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A255536 Indices of primes in the 9th-order Fibonacci number sequence, A251752.

Original entry on oeis.org

10, 11, 21, 29, 301, 57089
Offset: 1

Views

Author

Robert Price, Feb 24 2015

Keywords

Comments

a(7) > 2*10^5.

Links

Crossrefs

Cf. A001590, A001631, A100683, A231574, A231575, A232542, A214899, A230607, A020992, A232498, A214727, A081172, A214752, A141523, A214825, A235862, A000288, A000322, A000383, A249413, A060455, A079262, A251752.

Programs

  • Mathematica
    a={0,1,0,0,0,0,0,0,0}; step=9; lst={}; For[n=step,n<=1000,n++, sum=Plus@@a; If[PrimeQ[sum], AppendTo[lst,n]]; a=RotateLeft[a]; a[[step]]=sum]; lst

A251746 9-step Fibonacci sequence starting with 0,0,0,0,0,0,0,1,0.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 4, 8, 16, 32, 64, 128, 255, 510, 1019, 2036, 4068, 8128, 16240, 32448, 64832, 129536, 258817, 517124, 1033229, 2064422, 4124776, 8241424, 16466608, 32900768, 65736704, 131343872, 262428927, 524340730, 1047648231, 2093232040
Offset: 0

Views

Author

Arie Bos, Dec 07 2014

Keywords

Comments

a(n+9) equals the number of n-length binary words avoiding runs of zeros of lengths 9i+8, (i=0,1,2,...). - Milan Janjic, Feb 26 2015

Links

Crossrefs

Other 9-step Fibonacci sequences are A104144, A105755, A127193, A251747, A251748, A251749, A251750, A251751, A251752.
Cf. A255530 (Indices of primes in this sequence).

Programs

  • Mathematica
    LinearRecurrence[Table[1, {9}], {0, 0, 0, 0, 0, 0, 0, 1, 0}, 44] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+9) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7)+a(n+8).
G.f.: x^7*(x-1)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - R. J. Mathar, Mar 28 2025
a(n) = A104144(n+1)-A104144(n). - R. J. Mathar, Mar 28 2025

A251747 9-step Fibonacci sequence starting with 0,0,0,0,0,0,1,0,0.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1015, 2028, 4052, 8096, 16176, 32320, 64576, 129025, 257796, 515084, 1029153, 2056278, 4108504, 8208912, 16401648, 32770976, 65477376, 130825727, 261393658, 522272232, 1043515311, 2084974344
Offset: 0

Views

Author

Arie Bos, Dec 07 2014

Keywords

Links

Crossrefs

Other 9-step Fibonacci sequences are A104144, A105755, A127193, A251746, A251748, A251749, A251750, A251751, A251752.
Cf. A255531 (Indices of primes in this sequence).

Programs

  • Mathematica
    LinearRecurrence[Table[1, {9}], {0, 0, 0, 0, 0, 0, 1, 0, 0}, 44] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+9) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7)+a(n+8).
G.f.: x^6*(-1+x+x^2)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - R. J. Mathar, Mar 28 2025
a(n) = A104144(n+2)-A104144(n+1)-A104144(n). - R. J. Mathar, Mar 28 2025

A251749 9-step Fibonacci sequence starting with 0,0,0,0,1,0,0,0,0.

Original entry on oeis.org

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 4, 8, 16, 31, 62, 124, 248, 496, 991, 1980, 3956, 7904, 15792, 31553, 63044, 125964, 251680, 502864, 1004737, 2007494, 4011032, 8014160, 16012528, 31993503, 63923962, 127721960, 255192240, 509881616, 1018758495, 2035509496
Offset: 0

Views

Author

Arie Bos, Dec 07 2014

Keywords

Links

Crossrefs

Other 9-step Fibonacci sequences are A104144, A105755, A127193, A251746, A251747, A251748, A251750, A251751, A251752.
Cf. A255532 (Indices of primes in this sequence).

Programs

  • Mathematica
    LinearRecurrence[Table[1, {9}], {0, 0, 0, 0, 1, 0, 0, 0, 0}, 44] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+9) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7)+a(n+8).
G.f.: x^4*(-1+x+x^2+x^3+x^4)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - R. J. Mathar, Mar 28 2025

A251750 9-step Fibonacci sequence starting with 0,0,0,1,0,0,0,0,0.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 4, 8, 15, 30, 60, 120, 240, 480, 959, 1916, 3828, 7648, 15281, 30532, 61004, 121888, 243536, 486592, 972225, 1942534, 3881240, 7754832, 15494383, 30958234, 61855464, 123589040, 246934544, 493382496, 985792767, 1969643000
Offset: 0

Views

Author

Arie Bos, Dec 07 2014

Keywords

Links

Crossrefs

Other 9-step Fibonacci sequences are A104144, A105755, A127193, A251746, A251747, A251748, A251749, A251751, A251752.
Cf. A255533 (Indices of primes in this sequence).

Programs

  • Mathematica
    LinearRecurrence[Table[1, {9}], {0, 0, 0, 1, 0, 0, 0, 0, 0}, 44] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+9) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7)+a(n+8).
G.f.: x^3*(-1+x+x^2+x^3+x^4+x^5)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - R. J. Mathar, Mar 28 2025

A251751 9-step Fibonacci sequence starting with 0,0,1,0,0,0,0,0,0.

Original entry on oeis.org

0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 4, 7, 14, 28, 56, 112, 224, 448, 895, 1788, 3572, 7137, 14260, 28492, 56928, 113744, 227264, 454080, 907265, 1812742, 3621912, 7236687, 14459114, 28889736, 57722544, 115331344, 230435424, 460416768, 919926271, 1838039800
Offset: 0

Views

Author

Arie Bos, Dec 07 2014

Keywords

Links

Crossrefs

Other 9-step Fibonacci sequences are A104144, A105755, A127193, A251746, A251747, A251748, A251749, A251750, A251752.
Cf. A255534 (Indices of primes in this sequence).

Programs

  • Mathematica
    LinearRecurrence[Table[1, {9}], {0, 0, 1, 0, 0, 0, 0, 0, 0}, 44] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+9) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7)+a(n+8).
G.f.: x^2*(-1+x+x^2+x^3+x^4+x^5+x^6)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - R. J. Mathar, Mar 28 2025
a(n) = A172319(n-2)-2*A172319(n-3)+A172319(n-9). - R. J. Mathar, Mar 28 2025

A251748 9-step Fibonacci sequence starting with 0,0,0,0,0,1,0,0,0.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 4, 8, 16, 32, 63, 126, 252, 504, 1007, 2012, 4020, 8032, 16048, 32064, 64065, 128004, 255756, 511008, 1021009, 2040006, 4075992, 8143952, 16271856, 32511648, 64959231, 129790458, 259325160, 518139312, 1035257615, 2068475224
Offset: 0

Views

Author

Arie Bos, Dec 07 2014

Keywords

Comments

The only primes in this sequence whose indices are less than 2*10^5 are 2 and 65865769729, which correspond to indices of 10 and 45. - Robert Price, Feb 24 2015

Links

Crossrefs

Other 9-step Fibonacci sequences are A104144, A105755, A127193, A251746, A251747, A251749, A251750, A251751, A251752.

Programs

  • Mathematica
    LinearRecurrence[Table[1, {9}], {0, 0, 0, 0, 0, 1, 0, 0, 0}, 44] (* Michael De Vlieger, Dec 09 2014 *)

Formula

a(n+9) = a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)+a(n+5)+a(n+6)+a(n+7)+a(n+8).
G.f.: x^5*(-1+x+x^2+x^3)/(-1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9) . - R. J. Mathar, Mar 28 2025
Showing 1-7 of 7 results.

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