A281141 Least number b > 2 such that n*b^n - 1 is a prime number or 0 if no such b exists.

3, 3, 4, 0, 4, 3, 8, 4, 40, 3, 10, 8, 56, 4, 10, 0, 46, 3, 6, 6, 42, 51, 4, 6, 8, 67, 0, 18, 102, 18, 98, 34, 38, 6, 136, 0, 90, 17, 10, 3, 52, 5, 12, 8, 18, 3, 28, 132, 72, 165, 40, 657, 418, 101, 44, 205, 94, 9, 426, 10, 482, 36, 4, 0, 418, 252, 38, 7

Offset: 1

Author

Pierre CAMI, Jan 15 2017

Keywords

• nonn

Comments

By definition, if b < n+2 then the prime n*b^n - 1 is a generalized Woodall prime.

a(n) = 0 if n is in A097764. - Robert Israel, Jan 15 2017

From Robert G. Wilson v, Jan 20 2017: (Start)

Odd terms are about 3/14 of the total.

Records: 3, 4, 8, 40, 56, 67, 102, 136, 165, 657, 882, 1442, 4080, 5146, 6388, 8617, 9440, 13470, 19285, 22155, 947310, ..., .

Indices of prime terms: 1, 2, 6, 10, 18, 26, 38, 40, 42, 46, 54, 68, 84, 86, 110, ..., .

Indices of perfect power terms: 3, 5, 7, 8, 12, 14, 23, 25, 44, 58, 62, 63, 69, 107, ..., .

(End)

Examples

			1*3^1 - 1 = 2 prime, so a(1) = 3.
2*3^2 - 1 = 17 prime, so a(2) = 3.
3*4^3 - 1 = 191 prime, so a(3) = 4.
4*b^4 - 1 = (2*b^2)^2 - 1 = (2*b^2 + 1)*(2*b^2 - 1), which is always composite, so a(4) = 0.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1030 (first 500 terms from Pierre CAMI; a(456) corrected by Robert G. Wilson v)
• Pierre CAMI, PFGW Script

Crossrefs

Cf. A097764, A240235.

Programs

Mathematica

lst = {* the terms in A097764 *}; f[n_] := If[ MemberQ[lst, n], 0, Block[{b = 3}, While[ !PrimeQ[n*b^n - 1], b++]; b]]; Array[f, 70] (* Robert G. Wilson v, Jan 20 2017 *)