A281141 - OEIS

%I #43 Mar 02 2019 04:21:57

%S 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,

%T 18,98,34,38,6,136,0,90,17,10,3,52,5,12,8,18,3,28,132,72,165,40,657,

%U 418,101,44,205,94,9,426,10,482,36,4,0,418,252,38,7

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

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

%C a(n) = 0 if n is in A097764. - _Robert Israel_, Jan 15 2017

%C From _Robert G. Wilson v_, Jan 20 2017: (Start)

%C Odd terms are about 3/14 of the total.

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

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

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

%C (End)

%H Robert G. Wilson v, <a href="/A281141/b281141.txt">Table of n, a(n) for n = 1..1030</a> (first 500 terms from Pierre CAMI; a(456) corrected by Robert G. Wilson v)

%H Pierre CAMI, <a href="/A281141/a281141.txt">PFGW Script</a>

%e 1*3^1 - 1 = 2 prime, so a(1) = 3.

%e 2*3^2 - 1 = 17 prime, so a(2) = 3.

%e 3*4^3 - 1 = 191 prime, so a(3) = 4.

%e 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.

%t 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 *)

%Y Cf. A097764, A240235.

%K nonn

%O 1,1

%A _Pierre CAMI_, Jan 15 2017