A124151 Smallest k such that 1 + Sum{j=1..n} k^(2*j-1) is prime.

1, 1, 2, 1, 2, 1, 10, 2, 2, 1, 2, 1, 48, 182, 2, 1, 60, 1, 10, 42, 2, 1, 102, 12, 4, 12, 110, 1, 12, 1, 100, 5, 28, 18, 144, 1, 102, 9, 2, 1, 30, 1, 186, 110, 130, 1, 566, 23, 1234, 2, 12, 1, 336, 103, 142, 341, 1104, 1, 444, 1, 22, 119, 2, 45, 14, 1, 84, 23, 238, 1, 936, 1, 78, 12

Offset: 1

Author

Artur Jasinski, Dec 13 2006, Dec 14 2006

Keywords

• nonn

Comments

a(n) = 1 if and only if n is in A006093 (primes minus 1), so 1 occurs infinitely often.

Examples

			Consider n = 7. 1 + Sum{j=1...7} k^(2*j-1) evaluates to 8, 10923, 1793614, 71582789, 1271565756, 13433856703, 98907531458, 558482096649, 2573639151184, 10101010101011 for k = 1, ..., 10. Only the last of these numbers, 1+10+10^3+10^5+10^7+10^9+10^11+10^13 = 10101010101011, is prime, hence a(7) = 10.
		

Crossrefs

Cf. A006093, A124205-A124209, A124164, A124178, A124181, A124185-A124187, A124189, A124200, A124154, A124163.

Programs

Mathematica

f[n_] := Block[{k = 1}, While[ !PrimeQ[Sum[k^(2j - 1), {j, n}] + 1], k++ ]; k]; Array[f, 74] (* Robert G. Wilson v, Dec 17 2006 *)

PARI

a(n)={my(k=1);while(!isprime(1+sum(j=1,n,k^(2*j-1))),k++); k} \\ Klaus Brockhaus, Dec 16 2006

Extensions

Edited and extended by Klaus Brockhaus, Dec 16 2006