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

Author

Abhiram R Devesh, Apr 25 2015

Keywords

• nonn
• easy

Comments

This sequence is a subsequence of A002313 (Primes of form x^2 + y^2).

Examples

			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.
		

Links

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

Crossrefs

Cf. A002313 (Primes of form x^2 + y^2).

Programs

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**p0:
    a0, b0=sumpow(s0, 0, pw)
    a1, b1=sumpow(s0, 1, pw)
    if a0!=0 and a1!=0:
        print(s0)
    s0=sympy.nextprime(s0)