A279069 - OEIS

A279069

Smallest k such that 1 + p + p^2 + p^3 + ... + p^k is prime, where p is the n-th prime.

1, 2, 2, 4, 16, 4, 2, 18, 4, 4, 6, 12, 2, 4, 126, 10, 2, 6, 18, 2, 4, 4, 4, 2, 16, 2, 18, 16, 16, 22, 4, 2, 10, 162, 6, 12, 16, 6, 2, 2, 18, 16, 16, 4, 30, 576, 40, 238, 4, 10, 112, 4, 16, 6, 22, 4

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OFFSET

1,2

COMMENTS

Equivalently, smallest k such that (p^(k+1)-1)/(p-1) is prime, where p is the n-th prime.

For p prime, the sum of divisors of p^k is Sum_{j=0..k} p^j, so a(n) is the smallest k such that sigma(prime(n)^k) is prime, where sigma is the sum of divisors function A000203.

For the corresponding primes Sum_{j=0..k} p^j, see A279068.

a(57) > 10000. Next several terms after a(57) are 40, 4, a(60), 28, 2, 52, a(64), 108, 156, a(67), 4, 336; unknown terms a(60), a(64), and a(67) each exceed 5000.

LINKS

Table of n, a(n) for n=1..56.

CROSSREFS

Cf. A000203, A279068.

Sequence in context: A153965 A121221 A122598 * A257609 A087783 A176190

Adjacent sequences: A279066 A279067 A279068 * A279070 A279071 A279072

KEYWORD

nonn,more

AUTHOR

Jon E. Schoenfield, Dec 23 2016

STATUS

approved