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A145023
Primes p of the form 4k+1 for which s=5 is the least positive integer such that s*p - floor(sqrt(s*p))^2 is a perfect square.
13
353, 373, 449, 461, 521, 541, 593, 653, 673, 757, 769, 797, 821, 829, 941, 953, 1009, 1021, 1061, 1069, 1097, 1193, 1217, 1249, 1277, 1361, 1381, 1481, 1489, 1549, 1597, 1613, 1657, 1669, 1693, 1709, 1733, 1777, 1801, 1877, 1889, 1973, 2053, 2069, 2081
OFFSET
1,1
COMMENTS
Primes p == 1 (mod 4) such that A245474(p) = 5. These numbers are a subset of {A245440}. Curiosity: a(n) = A245440(n) for all n < 25. - Thomas Ordowski, Jul 22 2014
EXAMPLE
a(1)=353 since p=353 is the least prime of the form 4k+1 for which s*p - (floor(sqrt(s*p)))^2 is not a perfect square for s=1,...,4, but 5*p - (floor(sqrt(5*p)))^2 is a perfect square (for p=353 it is 1).
PROG
(PARI) s=[]; forprime(p=2, 3000, if(p%4==1 && !issquare(p-sqrtint(p)^2) && !issquare(2*p-sqrtint(2*p)^2) && !issquare(3*p-sqrtint(3*p)^2) && !issquare(4*p-sqrtint(4*p)^2) && issquare(5*p-sqrtint(5*p)^2), s=concat(s, p))); s \\ Colin Barker, Jul 23 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 29 2008
STATUS
approved