A059844 a(n) = smallest nonzero square x^2 such that n+x^2 is prime.

1, 1, 4, 1, 36, 1, 4, 9, 4, 1, 36, 1, 4, 9, 4, 1, 36, 1, 4, 9, 16, 1, 36, 49, 4, 81, 4, 1, 144, 1, 16, 9, 4, 9, 36, 1, 4, 9, 4, 1, 576, 1, 4, 9, 16, 1, 36, 25, 4, 9, 16, 1, 36, 25, 4, 81, 4, 1, 324, 1, 36, 9, 4, 9, 36, 1, 4, 81, 4, 1, 36, 1, 16, 9, 4, 25, 36, 1, 4, 9, 16, 1, 144, 25, 4, 81

Offset: 1

Author

Labos Elemer, Feb 26 2001

Keywords

• nonn

Comments

a(n) = 1 for n in A006093. - Robert Israel, Dec 31 2023

Examples

			a(24) = 49 because 49 + 24 = 73 is prime and 1 + 24 = 25, 4 + 24 = 28, 9 + 24 = 33, 16 + 24 = 40, 25 + 24 = 49, and 36 + 24 = 60 are composite.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002496, A006093, A056899, A049423, A005473, A056905, A056909.

Programs

Maple

f:= proc(n) local x;
 for x from 1 + (n mod 2) by 2  do
  if isprime(n+x^2) then return x^2 fi;
 od
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Dec 31 2023

Mathematica

sqs[n_]:=Module[{q=1},While[!PrimeQ[n+q],q=(Sqrt[q]+1)^2];q]; Array[ sqs,90] (* Harvey P. Dale, Aug 11 2017 *)

Formula

a(n) + n is the smallest prime of the form x^2 + n.