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

%I A059844 #17 Jan 01 2024 09:08:23
%S A059844 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,
%T A059844 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,
%U A059844 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
%N A059844 a(n) = smallest nonzero square x^2 such that n+x^2 is prime.
%C A059844 a(n) = 1 for n in A006093. - _Robert Israel_, Dec 31 2023
%H A059844 Robert Israel, <a href="/A059844/b059844.txt">Table of n, a(n) for n = 1..10000</a>
%F A059844 a(n) + n is the smallest prime of the form x^2 + n.
%e A059844 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.
%p A059844 f:= proc(n) local x;
%p A059844  for x from 1 + (n mod 2) by 2  do
%p A059844   if isprime(n+x^2) then return x^2 fi;
%p A059844  od
%p A059844 end proc:
%p A059844 f(1):= 1:
%p A059844 map(f, [$1..100]); # _Robert Israel_, Dec 31 2023
%t A059844 sqs[n_]:=Module[{q=1},While[!PrimeQ[n+q],q=(Sqrt[q]+1)^2];q]; Array[ sqs,90] (* _Harvey P. Dale_, Aug 11 2017 *)
%Y A059844 Cf. A002496, A006093, A056899, A049423, A005473, A056905, A056909.
%K A059844 nonn
%O A059844 1,3
%A A059844 _Labos Elemer_, Feb 26 2001