cp's OEIS Frontend

A352424 Numbers that can be written as sums of squares of consecutive primes in two ways.

%I A352424 #18 Apr 18 2024 06:11:00
%S A352424 14720439,16535628,34714710,40741208,61436388,603346308,1172360113,
%T A352424 1368156941,1574100889,1924496102,1989253499,2021860243,6774546339,
%U A352424 9770541610,12230855963,12311606487,12540842446,14513723777,26423329489,38648724198,47638558043,50195886916,50811319931,56449248367
%N A352424 Numbers that can be written as sums of squares of consecutive primes in two ways.
%H A352424 Michael S. Branicky, <a href="/A352424/b352424.txt">Table of n, a(n) for n = 1..991</a>
%H A352424 Cathal O'Sullivan, Jonathan P. Sorenson, and Aryn Stahl, <a href="https://arxiv.org/abs/2204.10930">An Algorithm to Find Sums of Consecutive Powers of Primes</a>, arXiv:2204.10930 [math.NT], 2022-2023. See 4.2 Duplicates p. 8-9.
%H A352424 Michael S. Branicky, <a href="/A352424/a352424.py.txt">Python Program</a>
%o A352424 (Python) # see link for a version suitable for producing b-file
%o A352424 from sympy import primerange, integer_nthroot
%o A352424 def aupto(limit):
%o A352424     adict = dict()
%o A352424     rootlimit = integer_nthroot(limit, 2)[0]
%o A352424     for x in primerange(2, rootlimit+1):
%o A352424         s = x**2
%o A352424         adict[s] = 1
%o A352424         for y in primerange(x+1, rootlimit+1):
%o A352424             s += y**2
%o A352424             if s <= limit:
%o A352424                 if s not in adict:
%o A352424                     adict[s] = 1
%o A352424                 else:
%o A352424                     adict[s] += 1
%o A352424             else:
%o A352424                 break
%o A352424     return sorted(s for s in adict if adict[s] == 2)
%o A352424 print(aupto(6*10**10)) # _Michael S. Branicky_, Apr 26 2022
%Y A352424 Cf. A001248, A340771.
%K A352424 nonn
%O A352424 1,1
%A A352424 _Michel Marcus_, Apr 26 2022