A231818 Least positive k such that k*n^n - 1 is a prime.

3, 1, 2, 5, 6, 3, 6, 39, 18, 6, 12, 19, 8, 23, 10, 3, 76, 13, 90, 26, 52, 45, 124, 12, 60, 27, 10, 99, 126, 11, 50, 27, 28, 59, 6, 80, 122, 71, 110, 21, 72, 111, 590, 147, 178, 84, 238, 12, 138, 236, 10, 53, 6, 60, 98, 72, 620, 30, 166, 5, 98, 18, 22, 384, 126

Offset

1,1

Comments

By Dirichlet's theorem on primes in arithmetic progressions, such a k always exists. - Robert Israel, Mar 04 2026

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Formula

a(n) = A053989(n^n). - Robert Israel, Mar 04 2026

Maple

f:= proc(n) local r, k;
     r:= n^n;
     for k from 1 do if isprime(k*r-1) then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Mar 04 2026

Mathematica

Table[k = 1; While[! PrimeQ[k*n^n - 1], k++]; k, {n, 65}] (* T. D. Noe, Nov 15 2013 *)

Crossrefs

Cf. A035092 (least k such that k*(n^2)+1 is a prime).

Cf. A175763 (least k such that k*(n^n)+1 is a prime).

Cf. A035093 (least k such that k*n!+1 is a prime).

Cf. A193807 (least k such that n*(k^2)+1 is a prime).

Cf. A231119 (least k such that n*(k^k)+1 is a prime).

Cf. A057217 (least k such that n*k!+1 is a prime).

Cf. A034693 (least k such that n*k +1 is a prime).

Cf. A231819 (least k such that k*(n^2)-1 is a prime).

Cf. A083663 (least k such that k*n!-1 is a prime).

Cf. A231734 (least k such that n*(k^2)-1 is a prime).

Cf. A231735 (least k such that n*(k^k)-1 is a prime).

Cf. A231820 (least k such that n*k!-1 is a prime).

Cf. A053989 (least k such that n*k -1 is a prime).

Sequence in context: A153091 A359753 A183386 * A280633 A084614 A050058

Adjacent sequences: A231815 A231816 A231817 * A231819 A231820 A231821

Keyword

nonn

Author

Alex Ratushnyak, Nov 13 2013

Status

approved