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 1-4 of 4 results.

A124257 Complement of A124168.

Original entry on oeis.org

6, 9, 10, 11, 12, 14, 17, 18, 19, 20, 22, 23, 25, 26, 27, 28, 30, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 58, 59, 60, 62, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96
Offset: 1

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Author

N. J. A. Sloane, following a suggestion of Jonathan Vos Post, Dec 15 2006

Keywords

A127232 Eulerian numbers A000295 appearing in the intersection of Fibonacci and Lucas sequences A124168 and A127208.

Original entry on oeis.org

1, 120, 524268, 140737488355280, 2596148429267413814265248164609936, 57896044618658097711785492504343953926634992332820282019728792003956564819712
Offset: 1

Views

Author

T. D. Noe, Jan 09 2007

Keywords

Comments

a(n) is common to the r-step Fibonacci sequence and the s-step Lucas sequence for s=A001792(n)-2 and r=s-n+1. See A127208 for more information about the intersection of Fibonacci and Lucas sequences.

Examples

			a(2)=120 appears in the 5-step Fibonacci sequence A001591 and the 6-step Lucas sequence A074584. a(3)=524268 appears in the 16-step Fibonacci sequence and the 18-step Lucas sequence.

Links

Crossrefs

Cf. A000295, A001591, A074584, A124168, A127208.

Programs

  • Magma
    [2^((n+2)*2^(n-1)-1)-(n+2)*2^(n-1): n in [1..7]]; // Vincenzo Librandi, Aug 26 2011
  • PARI
    a(n) = my(k=(n+2)*2^(n-1)); 2^(k-1)-k; \\ Michel Marcus, Mar 25 2016

Formula

a(n) = 2^(k-1)-k for k=A001792(n).

A127208 Union of all n-step Lucas sequences, that is, all sequences s(1-n) = s(2-n) = ... = s(-1) = -1, s(0) = n and for k > 0, s(k) = s(k-1) + ... + s(k-n).

Original entry on oeis.org

1, 3, 4, 7, 11, 15, 18, 21, 26, 29, 31, 39, 47, 51, 57, 63, 71, 76, 99, 113, 120, 123, 127, 131, 191, 199, 223, 239, 241, 247, 255, 322, 367, 439, 443, 475, 493, 502, 511, 521, 708, 815, 843, 863, 943, 983, 1003, 1013, 1023, 1364, 1365, 1499, 1695, 1871, 1959
Offset: 1

Views

Author

T. D. Noe, Jan 09 2007

Keywords

Comments

Noe and Post conjectured that the only positive terms that are common to any two distinct n-step Lucas sequences are the Mersenne numbers (A001348) that begin each sequence and 7 and 11 (in 2- and 3-step) and 5071 (in 3- and 4-step). The intersection of this sequence with the union of all the n-step Fibonacci sequences (A124168) appears to consist of 4, 21, 29, the Mersenne numbers 2^n-1 for all n and the infinite set of Eulerian numbers in A127232.

Links

Crossrefs

Cf. A227885.

Programs

  • Mathematica
    LucasSequence[n_,kMax_] := Module[{a,s,lst={}}, a=Join[Table[ -1,{n-1}],{n}]; While[s=Plus@@a; a=RotateLeft[a]; a[[n]]=s; s<=kMax, AppendTo[lst,s]]; lst]; nn=10; t={}; Do[t=Union[t,LucasSequence[n,2^(nn+1)]], {n,2,nn}]; t

Formula

Union(A000032, A001644, A073817, A074048, A074584, A104621, A105754, A105755,...)

A227880 Primes in the union of all n-Fibonacci sequences.

Original entry on oeis.org

2, 3, 5, 7, 13, 29, 31, 61, 89, 127, 149, 233, 401, 509, 773, 1021, 1597, 4093, 8191, 16381, 28657, 31489, 128257, 131071, 514229, 524287, 1048573, 4194301, 5976577, 16777213, 433494437, 536870909, 2147483647, 2971215073, 4293722117, 5350220959, 13435170943
Offset: 1

Views

Author

Robert Price, Oct 25 2013

Keywords

Links

Crossrefs

Cf. A124168, A000045, A000073, A000078, A001591, A001592, A124257.

Programs

  • Mathematica
    plst = {};plimit=10^39; For[n = 2, n ≤ 1 + Log[2, plimit], n++,flst = {};For[i = 1, i < n, i++, AppendTo[flst, 0]];AppendTo[flst, 1];For[k = 2, k ≤ 1 + Log[GoldenRatio, plimit*Sqrt[5] + 0.5], k++,sum = 0;For[j = 0, j < n, j++, sum = sum + flst[[j + k - 1]]];AppendTo[flst, sum];If[sum ≤ plimit && PrimeQ[sum], AppendTo[plst, sum]]]];Union[plst]

Formula

Primes in A124168.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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