cp's OEIS Frontend

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

%I A257118 #37 Jan 15 2025 17:48:44
%S A257118 89,389,397,449,661,757,761,929,997,1193,1201,1669,2213,2269,2293,
%T A257118 2593,2609,2617,2741,3037,3041,3209,3217,3413,3433,3449,3697,3877,
%U A257118 4397,4801,5189,5233,5237,5569,5689,5717,6101,6217,6389,6469,6733,6829,6833,6997,7529
%N A257118 Smallest of three consecutive prime numbers each of which is the sum of two squares.
%C A257118 This sequence is a subsequence of A257117.
%H A257118 Harvey P. Dale, <a href="/A257118/b257118.txt">Table of n, a(n) for n = 1..200</a>
%e A257118 389 = 10^2 + 17^2, 397 = 6^2 + 19^2, and 401 = 1^2 + 20^2, so 389 is a term.
%e A257118 397 = 6^2 + 19^2, 401 = 1^2 + 20^2, and 409 = 3^2 + 20^2, so 397 is a term.
%t A257118 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 *)
%o A257118 (Python)
%o A257118 # a(1) is not displayed.
%o A257118 import sympy
%o A257118 def sumpow(sn0, n, p):
%o A257118     af=0; bf=0; an=1
%o A257118     sn1=sn0+n
%o A257118     if n!=0:
%o A257118         sn1=sympy.nextprime(sn0, n)
%o A257118     while an**p<sn1:
%o A257118         bnsq=sn1-(an**p)
%o A257118         bn=sympy.ntheory.perfect_power(bnsq)
%o A257118         if bn!=False and list(bn)[1]==p:
%o A257118             af=an
%o A257118             bf=list(bn)[0]
%o A257118             an=sn1+100
%o A257118         an=an+1
%o A257118     return(af, bf)
%o A257118 s0=1; pw=2
%o A257118 while s0>0:
%o A257118     a0, b0=sumpow(s0, 0, pw)
%o A257118     a1, b1=sumpow(s0, 1, pw)
%o A257118     a2, b2=sumpow(s0, 2, pw)
%o A257118     if a0!=0 and a1!=0 and a2!=0:
%o A257118         print(s0)
%o A257118     s0=sympy.nextprime(s0)
%Y A257118 Cf. A064716 (Smallest member of three consecutive numbers).
%Y A257118 Cf. A257117 (Smallest member of two consecutive prime numbers).
%K A257118 nonn,easy
%O A257118 1,1
%A A257118 _Abhiram R Devesh_, Apr 25 2015
%E A257118 Corrected and extended by and prior b-file replaced by _Harvey P. Dale_, Jul 08 2018