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.

A078748 Duplicate of A051131.

Original entry on oeis.org

2, 5, 877, 27644437, 35742549198872617291353508656626642567
Offset: 1

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Author

Keywords

A051130 Indices of prime Bell numbers A000110.

Original entry on oeis.org

2, 3, 7, 13, 42, 55, 2841
Offset: 1

Views

Author

Ignacio Larrosa Cañestro

Keywords

Comments

Bell(2841) has been certified to be a prime using Primo. This took 17 months on a P3-800, a P4-2400 and finally a P4-2800. There are no other terms below 6000. - Ignacio Larrosa Cañestro, Feb 13 2004
The next term, if it exists, is > 50000. - Vaclav Kotesovec, May 18 2021
No other terms < 100000. - Mathieu Gouttenoire, Oct 31 2021

Examples

			The Bell numbers Bell(2)=2, Bell(3)=5, Bell(7)=877 etc. are primes.

Links

Crossrefs

Cf. A000110, A051131.

Programs

  • Magma
    [n: n in [0..1000]|IsPrime(Bell(n))]; // Vincenzo Librandi, Jan 30 2016
  • Mathematica
    Reap[For[n = 1, n <= 3000, n++, If[PrimeQ[BellB[n]], Print[n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Jun 05 2012 *)
Select[Range[2900],PrimeQ[BellB[#]]&] (* Harvey P. Dale, Nov 08 2012 *)

A322924 Sum of n-th Bell number and n-th Bell number written backwards.

Original entry on oeis.org

2, 2, 4, 10, 66, 77, 505, 1655, 4554, 95259, 695486, 754446, 12166721, 101089109, 414897413, 6841551376, 84604250548, 123761716632, 1633685476445, 13337764677442, 79077443378087, 632521435125225, 7744164113623377, 108500061705109490, 1428467362263664833
Offset: 0

Views

Author

Vincenzo Librandi, Mar 12 2019

Keywords

Comments

After 2, the next prime Bell number is a(110), which has 131 digits.

Examples

			a(4) = 66 because Bell(4) = 15 and 15 + 51 = 66.
a(5) = 77 because Bell(5) = 52 and 52 + 25 = 77.

Links

Crossrefs

Cf. A000110, A004098, A051131, A302092.

Programs

  • Magma
    [Bell(n) + Seqint(Reverse(Intseq(Bell(n)))): n in [0..30]];
  • Maple
    g:= proc(n) local L,i;
L:= convert(n,base,10);
n + add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
map(g @ combinat:-bell, [$0..30]); # Robert Israel, Mar 13 2019
  • Mathematica
    BellB[#] + FromDigits[Reverse[IntegerDigits[BellB[#]]]]&/@Range[0, 30]

Formula

a(n) = A000110(n) + A004098(n).
Showing 1-3 of 3 results.

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

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