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 1-1 of 1 results.

A240767 Numbers n such that n^k + (n-1)^k + ... + 3^k + 2^k is prime for some natural number k.

Original entry on oeis.org

2, 3, 4, 7, 8, 11, 12, 16
Offset: 1

Views

Author

Derek Orr, Apr 12 2014

Keywords

Comments

a(9) > 19. See A240766 for more information.
a(n) is also the n-values such that A240766(n) is nonzero.
It is known that a(n) must be == 3 mod 4 or 0 mod 4 (except a(1) = 2) due to the parity of the sum. If an n-value is congruent to 1 mod 4 or 2 mod 4, the sum will always be even and thus, not prime.
It is known that 31, 36, 40, 43, 47, 56, 67, 83, and 171 are members of this sequence.
If n-1 is not squarefree, then n is not a member of this sequence.

Examples

			2^k is prime for at least one k (and only one k in this instance; k = 1). Thus, 2 is a member of this sequence.
3^k+2^k is prime for at least one k (see A082101). Thus, 3 is a member of this sequence.

Crossrefs

Cf. A081507, A082101, A240766.

Programs

  • PARI
    a(n)=for(k=1,4000,if(ispseudoprime(sum(i=2,n,i^k)),return(k)))
n=1; while(n<200,if(a(n),print(a(n)));n+=1)
Showing 1-1 of 1 results.

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

Content is available under The OEIS End-User License Agreement.