A078770 a(n) = the least positive integer k such that k^2 + k + N is prime, where N is the n-th positive odd integer.

1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 2, 4, 1, 2, 1, 1, 5, 1, 2, 3, 1, 2, 2, 1, 1, 2, 4, 1, 2, 1, 1, 2, 7, 1, 5, 1, 2, 3, 1, 3, 2, 4, 1, 2, 1, 1, 2, 1, 1, 5, 1, 10, 3, 4, 3, 2, 7, 1, 3, 1, 2, 2, 1, 1, 3, 7, 2, 2, 1, 1, 2, 4, 1, 2, 4, 1, 5, 1, 2, 3, 1

Offset

1,4

Comments

k^2 + k + n for even n is always even and > 2, so is never prime.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

For n=1, k^2+k+1 is prime for k=1, since it is 3.
For n=7, k^2+k+7 is not prime for k=1, but is prime for k=2, since it is 13.

Mathematica

lpik[n_]:=Module[{k=1}, While[!PrimeQ[k^2+k+n], k++]; k]; Table[lpik[n], {n, 1, 181, 2}] (* Harvey P. Dale, Sep 24 2017 *)

Prog

(PARI) lista(nn) = {forstep (n=1, nn, 2, k = 1; while(! isprime(k*k + k + n), k++); print1(k, ", "); ); } \\ Michel Marcus, May 18 2013
(PARI) a(n)=my(k=1); while(!isprime(k^2+k+2*n-1), k++); k \\ Charles R Greathouse IV, May 19 2013

Crossrefs

Sequence in context: A210763 A281681 A218799 * A072038 A284315 A262928

Adjacent sequences: A078767 A078768 A078769 * A078771 A078772 A078773

Keyword

nonn

Author

Joseph L. Pe, Jan 09 2003

Status

approved