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 A363284 Numbers that are square or square pyramidal. 2
 0, 1, 4, 5, 9, 14, 16, 25, 30, 36, 49, 55, 64, 81, 91, 100, 121, 140, 144, 169, 196, 204, 225, 256, 285, 289, 324, 361, 385, 400, 441, 484, 506, 529, 576, 625, 650, 676, 729, 784, 819, 841, 900, 961, 1015, 1024, 1089, 1156, 1225, 1240, 1296, 1369, 1444, 1496 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This sequence essentially consists of the numbers in A363269 arranged in increasing order. Although A363269 is a linear recurrence sequence, it appears that this sequence is not. 4900 is the only nontrivial case of a square number that is also square pyramidal (proved by Watson). - Peter Munn, Jul 30 2023 REFERENCES W. Ljunggren, New solution of a problem proposed by E. Lucas, Norsk Mat. Tidsskr. 34 (1952), pp 65-72. David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, 1987, entry 24, p 101. LINKS Table of n, a(n) for n=1..54. Michael A. Bennett, Lucas' Square Pyramid Problem Revisited. E. Lucas, Problem 1180, Nouvelles Ann. Math. (2) 14 (1875), p 336. G. N. Watson, The problem of the square pyramid, Messenger of Mathematics 48 (1918), pp. 1-22. MATHEMATICA c[1] = 1; c[2] = 1; c[n_] := If[OddQ[n], c[n - 2] + n, c[n - 2] + c[n - 1]] u = Table[c[n], {n, 1, 120}] (* A363269 *) FindLinearRecurrence[u] Union[u] (* this sequence *) CROSSREFS Cf. A000290, A000330, A363269. Sequence in context: A287209 A038099 A243166 * A363269 A120740 A274282 Adjacent sequences: A363281 A363282 A363283 * A363285 A363286 A363287 KEYWORD nonn AUTHOR Clark Kimberling, May 25 2023 EXTENSIONS Name simplified and 0 prefixed to data by Peter Munn, Jul 30 2023 STATUS approved

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Last modified September 13 08:24 EDT 2024. Contains 375902 sequences. (Running on oeis4.)