OFFSET
1,1
COMMENTS
See the conjecture in the comment at A145047. In addition, I conjecture that for every such s there exist infinitely many primes of the form 4k+1.
PROG
(PARI) f(s)=forprime(p=2, , if(p%4>1 || !issquare(s*p-sqrtint(s*p)^2), next); for(i=1, s-1, if(issquare(i*p-sqrtint(i*p)^2), next(2))); return(p))
S=select(n->if(n%2==0, if(n%4, n/=2, return(0))); n==1||vecmax(factor(n)[, 1]%4)==1, vector(150, i, i));
apply(f, S) \\ Charles R Greathouse IV, Feb 07 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Oct 05 2008
EXTENSIONS
a(22) corrected by Charles R Greathouse IV, Feb 07 2013
STATUS
approved