A075556 Smallest prime p not occurring earlier such that p+n is a square, or 0 if no such p exists.

3, 2, 13, 5, 11, 19, 29, 17, 7, 71, 53, 37, 23, 67, 181, 0, 47, 31, 557, 61, 43, 59, 41, 97, 0, 199, 73, 197, 167, 139, 113, 89, 163, 191, 109, 0, 107, 83, 157, 401, 103, 79, 101, 317, 151, 179, 149, 241, 0, 239, 349, 173, 271, 307, 269, 233, 619, 383, 137, 229

Offset: 1

Author

Amarnath Murthy, Sep 23 2002

Keywords

• nonn

Comments

a(n)=0 or 2*sqrt(n)+1 for square n. Apparently the only cases where it is 2*sqrt(n)+1 are n=1, 4 and 9. - Ralf Stephan, Mar 30 2003, corrected by Robert Israel, Dec 07 2024

Links

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

Crossrefs

Cf. A075555, A075557.

Programs

Maple

for n from 1 to 100 do
  if issqr(n) then
    r:= sqrt(n);
    if isprime(2*r+1) and not assigned(S[2*r+1]) then R[n]:= 2*r+1; S[2*r+1]:= n else R[n] := 0 fi;
  else
    for k from ceil(sqrt(n)) do
      if not assigned(S[k^2-n]) and isprime(k^2-n) then R[n]:= k^2-n; S[k^2-n]:= n; break fi;
    od
  fi;
od:
seq(R[i],i=1..100); # Robert Israel, Dec 06 2024

PARI

v=vector(1000000); for(n=1, 100, f=0; forprime(p=2, 1000000, if(!v[p]&&issquare(p+n), f=p; break)); if(f, print1(f", "); v[f]=1, print1("0, ")));

Extensions

More terms from Ralf Stephan, Mar 30 2003