A145215 - OEIS

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A145215

a(n) is the minimal prime of the form 4k+1 for which s=A008784(n) is the minimal positive integer such that s*a(n)-floor(sqrt(s*a(n)))^2 is a square.

5, 41, 353, 1237, 2749, 3037, 10369, 6569, 27253, 38561, 14897, 33289, 27917, 171629, 143513, 76081, 37649, 373273, 399181, 63029, 133157, 637601, 425197, 94261, 499321, 910853, 229849, 149837

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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.

LINKS

Table of n, a(n) for n=1..28.

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