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A279069 Smallest k such that 1 + p + p^2 + p^3 + ... + p^k is prime, where p is the n-th prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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
CROSSREFS
Sequence in context: A153965 A121221 A122598 * A257609 A087783 A176190
KEYWORD
nonn,more
AUTHOR
Jon E. Schoenfield, Dec 23 2016
STATUS
approved

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Last modified March 29 05:43 EDT 2024. Contains 371264 sequences. (Running on oeis4.)