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A257118 Smallest of three consecutive prime numbers each of which is the sum of two squares. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is a subsequence of A257117.

LINKS

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

EXAMPLE

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.

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 *)

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)

....if a0!=0 and a1!=0 and a2!=0:

........print(s0)

....s0=sympy.nextprime(s0)

CROSSREFS

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

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

Sequence in context: A143828 A253140 A142448 * A244777 A107192 A061372

Adjacent sequences:  A257115 A257116 A257117 * A257119 A257120 A257121

KEYWORD

nonn,easy

AUTHOR

Abhiram R Devesh, Apr 25 2015

EXTENSIONS

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

STATUS

approved

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Last modified August 2 15:03 EDT 2021. Contains 346428 sequences. (Running on oeis4.)