|
%I #26 Jul 03 2016 00:14:43
%S 389,757,1193,2593,2609,3037,3209,3413,3433,5233,6829,7649,8669,8677,
%T 9157,9241,10169,10429,11173,11593,11597,11617,11621,11633,11657,
%U 12269,12277,12409,12413,12829,12841,15053,17389
%N Smallest member of four consecutive prime numbers each of which is the sum of two squares.
%C This sequence is a subset of A257118.
%H Abhiram R Devesh, <a href="/A257119/b257119.txt">Table of n, a(n) for n = 1..100</a>
%e a(1)=389 ; 389 = 10^2 + 17ยจ2; 397 = 6^2 + 19^2; 401 = 1^2 + 20^2; 409 = 3^2 + 20^2.
%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 ....a2,b2=sumpow(s0,2,pw)
%o ....a3,b3=sumpow(s0,3,pw)
%o ....if a0!=0 and a1!=0 and a2!=0 and a3!=0:
%o ........print(s0)
%o ....s0=sympy.nextprime(s0)
%Y Cf. A257117 (with two consecutive primes), A257118 (with three consecutive primes).
%K nonn,easy
%O 1,1
%A _Abhiram R Devesh_, Apr 25 2015
|
