

A281141


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


2



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
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OFFSET

1,1


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)


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


EXAMPLE

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.


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 *)


CROSSREFS

Cf. A097764, A240235.
Sequence in context: A230811 A117032 A243823 * A078911 A082899 A249491
Adjacent sequences: A281138 A281139 A281140 * A281142 A281143 A281144


KEYWORD

nonn


AUTHOR

Pierre CAMI, Jan 15 2017


STATUS

approved



