A257119 Smallest member of four consecutive prime numbers each of which is the sum of two squares.

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

Abhiram R Devesh, Table of n, a(n) for n = 1..100

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).

Sequence in context: A154624 A052353 A355651 * A298238 A299364 A299133

Adjacent sequences: A257116 A257117 A257118 * A257120 A257121 A257122

Keyword

nonn,easy

Author

Abhiram R Devesh, Apr 25 2015

Status

approved