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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
OFFSET
1,1
COMMENTS
This sequence is a subset of A257118.
LINKS
EXAMPLE
a(1)=389 ; 389 = 10^2 + 17ยจ2; 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).
Sequence in context: A154624 A052353 A355651 * A298238 A299364 A299133
KEYWORD
nonn,easy
AUTHOR
Abhiram R Devesh, Apr 25 2015
STATUS
approved