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A257117
Smaller of two consecutive primes each of which is the sum of two squares.
3
37, 109, 193, 229, 277, 313, 349, 389, 397, 401, 449, 457, 509, 613, 661, 673, 701, 757, 761, 769, 797, 853, 929, 937, 997, 1009, 1093, 1109, 1193, 1201, 1213, 1237, 1373, 1429, 1489, 1549, 1597, 1609, 1637, 1669
OFFSET
1,1
COMMENTS
This sequence is a subsequence of A002313 (Primes of form x^2 + y^2).
LINKS
EXAMPLE
37 = 1^2 + 6^2 and 41 = 4^2 + 5^2, so 37 is a term.
109 = 3^2 + 10^2 and 113 = 7^2 + 8^2, so 109 is a term.
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)
if a0!=0 and a1!=0:
print(s0)
s0=sympy.nextprime(s0)
CROSSREFS
Cf. A002313 (Primes of form x^2 + y^2).
Sequence in context: A142051 A282852 A171833 * A033215 A195316 A176549
KEYWORD
nonn,easy
AUTHOR
Abhiram R Devesh, Apr 25 2015
STATUS
approved