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A240767
Numbers n such that n^k + (n-1)^k + ... + 3^k + 2^k is prime for some natural number k.
1
2, 3, 4, 7, 8, 11, 12, 16
OFFSET
1,1
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.
EXAMPLE
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.
PROG
(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)
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Derek Orr, Apr 12 2014
STATUS
approved