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

1,1

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

Prog

(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

Crossrefs

Cf. A001248, A340771.

Sequence in context: A205413 A186067 A183661 * A267361 A015364 A081640

Adjacent sequences: A352421 A352422 A352423 * A352425 A352426 A352427

Keyword

nonn

Author

Michel Marcus, Apr 26 2022

Status

approved