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%I #29 May 09 2021 18:33:08
%S 37,109,193,229,277,313,349,389,397,401,449,457,509,613,661,673,701,
%T 757,761,769,797,853,929,937,997,1009,1093,1109,1193,1201,1213,1237,
%U 1373,1429,1489,1549,1597,1609,1637,1669
%N Smaller of two consecutive primes each of which is the sum of two squares.
%C This sequence is a subsequence of A002313 (Primes of form x^2 + y^2).
%H Abhiram R Devesh, <a href="/A257117/b257117.txt">Table of n, a(n) for n = 1..1000</a>
%e 37 = 1^2 + 6^2 and 41 = 4^2 + 5^2, so 37 is a term.
%e 109 = 3^2 + 10^2 and 113 = 7^2 + 8^2, so 109 is a term.
%o (Python)
%o import sympy
%o def sumpow(sn0,n,p):
%o ....af=0;bf=0;an=1
%o ....sn1=sn0+n
%o ....if n!=0:
%o ........sn1=sympy.nextprime(sn0,n)
%o ....while an**p<sn1:
%o ........bnsq=sn1-(an**p)
%o ........bn=sympy.ntheory.perfect_power(bnsq)
%o ........if bn!=False and list(bn)[1]==p:
%o ............af=an
%o ............bf=list(bn)[0]
%o ............an=sn1+100
%o ........an=an+1
%o ....return(af,bf)
%o s0=1; pw=2
%o while s0>0:
%o ....a0,b0=sumpow(s0,0,pw)
%o ....a1,b1=sumpow(s0,1,pw)
%o ....if a0!=0 and a1!=0:
%o ........print(s0)
%o ....s0=sympy.nextprime(s0)
%Y Cf. A002313 (Primes of form x^2 + y^2).
%K nonn,easy
%O 1,1
%A _Abhiram R Devesh_, Apr 25 2015
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