A257118 Smallest of three consecutive prime numbers each of which is the sum of two squares.

89, 389, 397, 449, 661, 757, 761, 929, 997, 1193, 1201, 1669, 2213, 2269, 2293, 2593, 2609, 2617, 2741, 3037, 3041, 3209, 3217, 3413, 3433, 3449, 3697, 3877, 4397, 4801, 5189, 5233, 5237, 5569, 5689, 5717, 6101, 6217, 6389, 6469, 6733, 6829, 6833, 6997, 7529

Offset: 1

Author

Abhiram R Devesh, Apr 25 2015

Keywords

• nonn
• easy

Comments

This sequence is a subsequence of A257117.

Examples

			389 = 10^2 + 17^2, 397 = 6^2 + 19^2, and 401 = 1^2 + 20^2, so 389 is a term.
397 = 6^2 + 19^2, 401 = 1^2 + 20^2, and 409 = 3^2 + 20^2, so 397 is a term.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A064716 (Smallest member of three consecutive numbers).

Cf. A257117 (Smallest member of two consecutive prime numbers).

Programs

Mathematica

Prime/@SequencePosition[Table[If[Count[IntegerPartitions[n,{2}],?(AllTrue[ Sqrt[#],IntegerQ]&)]>0,1,0],{n,Prime[Range[3000]]}],{1,1,1},Overlaps-> All] [[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale, Jul 08 2018 *)

Python

# a(1) is not displayed.
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)
    a2, b2=sumpow(s0, 2, pw)
    if a0!=0 and a1!=0 and a2!=0:
        print(s0)
    s0=sympy.nextprime(s0)

Extensions

Corrected and extended by and prior b-file replaced by Harvey P. Dale, Jul 08 2018