

A257119


Smallest member of four consecutive prime numbers each of which is the sum of two squares.


1



389, 757, 1193, 2593, 2609, 3037, 3209, 3413, 3433, 5233, 6829, 7649, 8669, 8677, 9157, 9241, 10169, 10429, 11173, 11593, 11597, 11617, 11621, 11633, 11657, 12269, 12277, 12409, 12413, 12829, 12841, 15053, 17389
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

This sequence is a subset of A257118.


LINKS



EXAMPLE

a(1)=389 ; 389 = 10^2 + 17¨2; 397 = 6^2 + 19^2; 401 = 1^2 + 20^2; 409 = 3^2 + 20^2.


PROG

(Python)
import sympy
def sumpow(sn0, n, p):
....af=0; bf=0; an=1
....sn1=sn0+n
....if n!=0:
........sn1=sympy.nextprime(sn0, n)
....while an**p<sn1:
........bnsq=sn1(an**p)
........bn=sympy.ntheory.perfect_power(bnsq)
........if bn!=False and list(bn)[1]==p:
............af=an
............bf=list(bn)[0]
............an=sn1+100
........an=an+1
....return(af, bf)
s0=1; pw=2
while s0>0:
....a0, b0=sumpow(s0, 0, pw)
....a1, b1=sumpow(s0, 1, pw)
....a2, b2=sumpow(s0, 2, pw)
....a3, b3=sumpow(s0, 3, pw)
....if a0!=0 and a1!=0 and a2!=0 and a3!=0:
........print(s0)
....s0=sympy.nextprime(s0)


CROSSREFS

Cf. A257117 (with two consecutive primes), A257118 (with three consecutive primes).


KEYWORD

nonn,easy


AUTHOR



STATUS

approved



