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 1-3 of 3 results.

A098166 a(n) is the prime index of the Lesser Fortunate number A055211(n), or 0 if A055211(n) is not a prime.

Original entry on oeis.org

2, 4, 5, 6, 7, 10, 9, 14, 13, 21, 17, 15, 24, 19, 21, 28, 24, 26, 31, 25, 23, 24, 25, 54, 32, 30, 36, 56, 54, 48, 41, 77, 60, 36, 45, 40, 52, 51, 43, 48, 48, 62, 108, 62, 88, 49, 64, 74, 55, 63, 65, 111, 69, 66, 63, 123, 91, 66, 83, 92, 97, 110, 67, 75, 99, 87
Offset: 2

Views

Author

Pierre CAMI, Aug 30 2004

Keywords

Links

Crossrefs

Cf. A000720, A055211, A098167.

Programs

  • PARI
    a(n) = {my(k = prod(j=1, n, prime(j))); p = k-precprime(k-2); if(isprime(p), primepi(p), 0); } \\ Jinyuan Wang, Oct 02 2019

Formula

a(n) = A000720(A055211(n)) iff A055211(n) is a prime. - Michel Marcus, Oct 05 2019

Extensions

Name edited by and more terms from Jinyuan Wang, Oct 02 2019

A098168 Prime index j such that prime(j) = the n-th fortunate number, A005235(n).

Original entry on oeis.org

2, 3, 4, 6, 9, 7, 8, 9, 12, 18, 19, 18, 20, 15, 28, 17, 18, 29, 24, 27, 22, 36, 45, 26, 27, 51, 48, 31, 48, 43, 38, 50, 117, 52, 37, 39, 85, 52, 46, 43, 46, 76, 51, 133, 65, 137, 111, 65, 76, 62, 86, 67, 61, 59, 58, 79, 63, 67, 75, 94, 67, 64, 78, 67, 71, 81, 82, 153, 101, 221
Offset: 1

Views

Author

Pierre CAMI, Aug 30 2004

Keywords

Links

Crossrefs

Cf. A005235, A055211, A098166, A098167.

Programs

  • Mathematica
    NextPrime[n_Integer] := Block[{k}, k = n + 1; While[ !PrimeQ[k], k++ ]; k]; Fortunate[n_Integer] := Block[{p = Product[Prime[i], {i, 1, n}] + 1, q}, q = NextPrime[p]; q - p + 1]; Table[ PrimePi[ Fortunate[n]], {n, 70}] (* Robert G. Wilson v, Sep 04 2004 *)

Extensions

More terms from Robert G. Wilson v, Sep 04 2004
Better definition from R. J. Mathar, Oct 28 2007

A098169 a(n) = Sum_{i=1..n} A098168(i).

Original entry on oeis.org

2, 5, 9, 15, 24, 31, 39, 48, 60, 78, 97, 115, 135, 150, 178, 195, 213, 242, 266, 293, 315, 351, 396, 422, 449, 500, 548, 579, 627, 670, 708, 758, 875, 927, 964, 1003, 1088, 1140, 1186, 1229, 1275, 1351, 1402, 1535, 1600, 1737, 1848, 1913, 1989, 2051, 2137, 2204
Offset: 1

Views

Author

Pierre CAMI, Aug 30 2004

Keywords

Crossrefs

Cf. A005235, A055211, A098166, A098167, A098168.

Programs

  • Mathematica
    NextPrime[n_Integer] := Block[{k}, k = n + 1; While[ !PrimeQ[k], k++ ]; k]; Fortunate[n_Integer] := Block[{p = Product[Prime[i], {i, 1, n}] + 1, q}, q = NextPrime[p]; q - p + 1]; t = Table[ PrimePi[ Fortunate[n]], {n, 70}]; Table[Plus @@ Take[t, n], {n, 52}] (* Robert G. Wilson v, Sep 04 2004 *)

Formula

Conjecture: a(n)/triangular(n) -> Log(e*Pi/2).

Extensions

More terms from Robert G. Wilson v, Sep 04 2004
Showing 1-3 of 3 results.

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

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