A240235 -id:A240235 - cp's OEIS frontend

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

Pierre CAMI, Jan 15 2017

nonn

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)

			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.

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

Cf. A097764, A240235.

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 *)

A327661 Least number k > n - 2 such that k*n^k - 1 is prime.

Original entry on oeis.org

3, 2, 2, 3, 8, 19, 18, 7, 10, 11, 252, 43, 563528, 98, 14, 167, 18, 28, 410, 44, 200, 140, 29028, 124, 68, 79, 2420, 47, 26850, 63, 2454, 140, 42, 164, 38, 62, 740, 67, 448, 51, 84, 135, 404882, 43, 84, 140, 140, 115, 710, 2390, 46640, 261, 60, 72, 2064, 414

Offset: 1

Jeppe Stig Nielsen, Sep 21 2019

Different version of A240235. Some authors, like Caldwell (link), require that k + 2 > n before they use the term generalized Woodall for a prime of form k*n^k - 1.

			To find a(11), consider numbers k*11^k - 1 where k > 9. The first time it is prime, is for k = 252, so a(11) = 252.

Jeppe Stig Nielsen, Table of n, a(n) for n = 1..144
Chris K. Caldwell, The Top Twenty: Generalized Woodall.

Cf. A240235, A327660, A240234.

for(b=1,+oo,for(k=b-1,+oo,if(ispseudoprime(k*b^k-1),print1(k,", ");next(2))))

A327660 Least number k > n - 2 such that k*n^k + 1 is prime.

Original entry on oeis.org

1, 1, 2, 3, 1242, 91, 34, 17, 12382, 9, 10, 247

Offset: 1

Jeppe Stig Nielsen, Sep 21 2019

Different version of A240234. Some authors, like Caldwell (link), require that k + 2 > n before they use the term generalized Cullen for a prime of form k*n^k + 1.

			To find a(9), consider numbers k*9^k + 1 where k > 7. The first time it is prime, is for k = 12382, so a(9) = 12382.

Chris K. Caldwell, The Top Twenty: Generalized Cullen.

Cf. A240234, A327661, A240235.

for(b=1,+oo,for(k=b-1,+oo,if(ispseudoprime(k*b^k+1),print1(k,", ");next(2))))

cp's OEIS Frontend

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

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A327661 Least number k > n - 2 such that k*n^k - 1 is prime.

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PARI

A327660 Least number k > n - 2 such that k*n^k + 1 is prime.

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PARI