cp's OEIS Frontend

A257117 Smaller of two consecutive primes each of which is the sum of two squares.

%I A257117 #33 Oct 11 2024 16:11:01
%S A257117 37,109,193,229,277,313,349,389,397,401,449,457,509,613,661,673,701,
%T A257117 757,761,769,797,853,929,937,997,1009,1093,1109,1193,1201,1213,1237,
%U A257117 1373,1429,1489,1549,1597,1609,1637,1669
%N A257117 Smaller of two consecutive primes each of which is the sum of two squares.
%C A257117 This sequence is a subsequence of A002313 (Primes of form x^2 + y^2).
%H A257117 Abhiram R Devesh, <a href="/A257117/b257117.txt">Table of n, a(n) for n = 1..1000</a>
%e A257117 37 = 1^2 + 6^2 and 41 = 4^2 + 5^2, so 37 is a term.
%e A257117 109 = 3^2 + 10^2 and 113 = 7^2 + 8^2, so 109 is a term.
%o A257117 (Python)
%o A257117 import sympy
%o A257117 def sumpow(sn0, n, p):
%o A257117     af=0; bf=0; an=1
%o A257117     sn1=sn0+n
%o A257117     if n!=0:
%o A257117         sn1=sympy.nextprime(sn0, n)
%o A257117     while an**p<sn1:
%o A257117         bnsq=sn1-(an**p)
%o A257117         bn=sympy.ntheory.perfect_power(bnsq)
%o A257117         if bn!=False and list(bn)[1]==p:
%o A257117             af=an
%o A257117             bf=list(bn)[0]
%o A257117             an=sn1+100
%o A257117         an=an+1
%o A257117     return(af, bf)
%o A257117 s0=1; pw=2
%o A257117 while s0>0:
%o A257117     a0, b0=sumpow(s0, 0, pw)
%o A257117     a1, b1=sumpow(s0, 1, pw)
%o A257117     if a0!=0 and a1!=0:
%o A257117         print(s0)
%o A257117     s0=sympy.nextprime(s0)
%Y A257117 Cf. A002313 (Primes of form x^2 + y^2).
%K A257117 nonn,easy
%O A257117 1,1
%A A257117 _Abhiram R Devesh_, Apr 25 2015