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 A368590 Numbers k such that all of k, k+1 and k+2 are the sums of consecutive squares. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 12 22:20 EDT 2024. Contains 375855 sequences. (Running on oeis4.)