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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

%I

%S 353,373,449,461,521,541,593,653,673,757,769,797,821,829,941,953,1009,

%T 1021,1061,1069,1097,1193,1217,1249,1277,1361,1381,1481,1489,1549,

%U 1597,1613,1657,1669,1693,1709,1733,1777,1801,1877,1889,1973,2053,2069,2081

%N 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.

%C 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

%e 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).

%o (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

%Y Cf. A002144, A145016, A145022, A245440, A245474.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Sep 29 2008

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Last modified July 29 14:30 EDT 2021. Contains 346346 sequences. (Running on oeis4.)