A352423 Numbers that are the sum of some number of consecutive prime cubes.

8, 27, 35, 125, 152, 160, 343, 468, 495, 503, 1331, 1674, 1799, 1826, 1834, 2197, 3528, 3871, 3996, 4023, 4031, 4913, 6859, 7110, 8441, 8784, 8909, 8936, 8944, 11772, 12167, 13969, 15300, 15643, 15768, 15795, 15803, 19026, 23939, 24389, 26136, 27467, 27810, 27935, 27962, 27970, 29791

Offset

1,1

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

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 S3 p. 10.

Prog

(PARI) lista(nn) = {my(list = List(), ip = primepi(nn), vp = primes(ip)); for(i=1, ip, my(s=vp[i]^3); listput(list, s); for (j=i+1, ip, s += vp[j]^3; if (s >vp[ip]^3, break); listput(list, s); ); ); Vec(vecsort(list, , 8)); }
(Python)
import heapq
from sympy import prime
from itertools import islice
def agen(): # generator of terms
    p = prime(1)**3; h = [(p, 1, 1)]; nextcount = 2
    while True:
        (v, s, l) = heapq.heappop(h)
        yield v
        if v >= p:
            p += prime(nextcount)**3
            heapq.heappush(h, (p, 1, nextcount))
            nextcount += 1
        v -= prime(s)**3; s += 1; l += 1; v += prime(l)**3
        heapq.heappush(h, (v, s, l))
print(list(islice(agen(), 47))) # Michael S. Branicky, Apr 26 2022

Crossrefs

Cf. A030078, A034707, A340771.

Sequence in context: A373144 A373373 A213519 * A371955 A066215 A086213

Adjacent sequences: A352420 A352421 A352422 * A352424 A352425 A352426

Keyword

nonn

Author

Michel Marcus, Apr 26 2022

Status

approved