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.

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

Links

Table of n, a(n) for n=1..45.

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

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

Sequence in context: A156177 A104160 A245440 * A343714 A343715 A177678

Adjacent sequences: A145020 A145021 A145022 * A145024 A145025 A145026

Keyword

nonn

Author

Vladimir Shevelev, Sep 29 2008

Status

approved