A257117 Smaller of two consecutive primes each of which is the sum of two squares.

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

Abhiram R Devesh, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A257114 A257115 A257116 * A257118 A257119 A257120

Keyword

nonn,easy

Author

Abhiram R Devesh, Apr 25 2015

Status

approved