A097350 -id:A097350

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A097349

Numbers n such that (Sum (2k)^k, k=1..n) + 1 is prime.

+10
1

1, 2, 13, 72, 318, 13583

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OFFSET

1,2

COMMENTS

Some of the larger entries may only correspond to probable primes.

The numbers produced by 72 and 318 have now been certified prime by Primo. 13583, found by PrimeForm using recurrence mode, corresponds to a 60228-digit probable prime. - Rick L. Shepherd, Apr 29 2006

LINKS

Table of n, a(n) for n=1..6.

EXAMPLE

13 is a term as 2^1 + 4^2 + 6^3 + 8^4 + 10^5 + 12^6 + 14^7 + 16^8 + 18^9 + 20^10 + 22^11 + 24^12 + 26^13 + 1 = 2518267981703965963, which is prime (certified with Primo).

PROG

(PARI) s=1; for(k=1, 700, s=s+(2*k)^k; if(isprime(s), print1(k, ", ")))

CROSSREFS

Cf. A073825 (Sum k^k, k=1..n, is prime), A097350 ((Sum (2k)^k, k=1..n) - 1 is prime).

KEYWORD

more,nonn

AUTHOR

Rick L. Shepherd, Aug 07 2004

EXTENSIONS

One more term from Rick L. Shepherd, Apr 29 2006

STATUS

approved

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