A035092 Smallest k such that (n^2)*k + 1 is prime.

1, 1, 2, 1, 4, 1, 4, 3, 2, 1, 6, 3, 4, 1, 8, 1, 12, 4, 30, 1, 2, 3, 24, 1, 18, 1, 2, 4, 12, 2, 16, 12, 2, 3, 6, 1, 4, 13, 6, 1, 10, 2, 12, 6, 2, 6, 4, 8, 6, 9, 6, 9, 28, 1, 4, 1, 10, 3, 6, 4, 46, 4, 4, 3, 4, 1, 4, 3, 22, 6, 10, 2, 4, 1, 2, 7, 22, 3, 6, 4, 6, 3, 10, 1, 4, 3, 2, 4, 6, 1, 10, 4, 2, 1

Offset

1,3

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primes in arithmetic progressions

Example

a(40) = 1 because in 1600k + 1 at k = 1, 1601 is the smallest prime;
a(61) = 46 because in the 46*46*k + 1 sequence the first prime appears at k = 46; it is 171167.

Mathematica

Table[k = 1; While[! PrimeQ[k (n^2) + 1], k++]; k, {n, 94}] (* Michael De Vlieger, Dec 17 2016 *)

Prog

(PARI)
a(n)=k=1; while(!isprime(k*n^2+1), k++); k
vector(100, n, a(n)) \\ Derek Orr, Oct 01 2014

Crossrefs

Analogous case is A034693. See also A005574 and A002496.

Sequence in context: A072721 A339792 A285711 * A160598 A107457 A112350

Adjacent sequences: A035089 A035090 A035091 * A035093 A035094 A035095

Keyword

nonn,easy

Author

Labos Elemer

Status

approved