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

14720439, 16535628, 34714710, 40741208, 61436388, 603346308, 1172360113, 1368156941, 1574100889, 1924496102, 1989253499, 2021860243, 6774546339, 9770541610, 12230855963, 12311606487, 12540842446, 14513723777, 26423329489, 38648724198, 47638558043, 50195886916, 50811319931, 56449248367

Offset: 1

Author

Michel Marcus, Apr 26 2022

Keywords

• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..991
• Cathal O'Sullivan, Jonathan P. Sorenson, and Aryn Stahl, An Algorithm to Find Sums of Consecutive Powers of Primes, arXiv:2204.10930 [math.NT], 2022-2023. See 4.2 Duplicates p. 8-9.
• Michael S. Branicky, Python Program

Crossrefs

Cf. A001248, A340771.

Programs

Python

# see link for a version suitable for producing b-file
from sympy import primerange, integer_nthroot
def aupto(limit):
    adict = dict()
    rootlimit = integer_nthroot(limit, 2)[0]
    for x in primerange(2, rootlimit+1):
        s = x**2
        adict[s] = 1
        for y in primerange(x+1, rootlimit+1):
            s += y**2
            if s <= limit:
                if s not in adict:
                    adict[s] = 1
                else:
                    adict[s] += 1
            else:
                break
    return sorted(s for s in adict if adict[s] == 2)
print(aupto(6*10**10)) # Michael S. Branicky, Apr 26 2022