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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS 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 Cf. A081507, A082101, A240766. Sequence in context: A285506 A188190 A026808 * A342028 A284937 A271441 Adjacent sequences:  A240764 A240765 A240766 * A240768 A240769 A240770 KEYWORD nonn,hard,more AUTHOR Derek Orr, Apr 12 2014 STATUS approved

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Last modified January 24 15:50 EST 2022. Contains 350541 sequences. (Running on oeis4.)