A368590 Numbers k such that all of k, k+1 and k+2 are the sums of consecutive squares.

728, 1013, 2813, 3309, 4323, 4899, 12438, 21259, 23113, 31394, 35719, 37812, 38023, 111894, 143449, 194053, 418613, 418614, 487368, 535309, 2232593, 2452644, 2490669, 9226854, 17367998, 19637644, 20341453, 28553671, 33406839, 174398434, 468936719, 1468970139, 2136314464

Offset

1,1

Comments

418613 is the smallest k such that k through k + 3 are the sums of consecutive squares.

After an idea by Allan C. Wechsler.

a(30)-a(33) were calculated using the b-file at A368570.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..94 (terms 1..74 from Frank A. Stevenson)

David A. Corneth, PARI program

Example

728 is in the sequence via 728 = 7^2 + 8^2 + 9^2 + 10^2 + 11^2 + 12^2 + 13^2, 729 = 27^2 and 730 = 10^2 + 11^2 + 12^2 + 13^2 + 14^2.

Prog

(PARI) \\ See PARI program
(Python)
import heapq
from itertools import islice
def agen(): # generator of terms
    m = 1; h = [(m, 1, 1)]; nextcount = 2
    v1 = v2 = -1
    while True:
        (v, s, l) = heapq.heappop(h)
        if v != v1:
            if v2 + 2 == v1 + 1 == v: yield v2
            v2, v1 = v1, v
        if v >= m:
            m += nextcount*nextcount
            heapq.heappush(h, (m, 1, nextcount))
            nextcount += 1
        v -= s*s; s += 1; l += 1; v += l*l
        heapq.heappush(h, (v, s, l))
print(list(islice(agen(), 33))) # Michael S. Branicky, Jan 01 2024

Crossrefs

Subsequence of A034705 and of A368570.

Sequence in context: A056084 A191345 A345744 * A023704 A043487 A158395

Adjacent sequences: A368587 A368588 A368589 * A368591 A368592 A368593

Keyword

nonn

Author

David A. Corneth, Dec 31 2023

Status

approved