A108394 Least k for which f(k) = (1 + f(0)^n + f(1)^n + ... + f(k-1)^n)/k, f(0) = 1, is nonintegral.

43, 89, 97, 214, 19, 239, 37, 79, 83, 239, 31, 431, 19, 79, 23, 827, 43, 173, 31, 103, 94, 73, 19, 243, 141, 101, 53, 811, 47, 1077, 19, 251, 29, 311, 134, 71, 23, 86, 43, 47, 19, 419, 31, 191, 83, 337, 59, 1559, 19, 127, 109, 163, 67, 353, 83, 191, 83, 107, 19, 503

Offset

2,1

References

Ian Stewart, Professor Stewart's Hoard of Mathematical Treasures, "Life, Recursion and Everything", Basic Books, NY, 2009, p. 239-240.

Links

Table of n, a(n) for n=2..61.

R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]

Rinnosuke Matsuhira, Toshiki Matsusaka, and Koki Tsuchida, How long can k-Göbel sequences remain integers?, arXiv:2307.09741 [math.NT], 2023.

Alex Stone, The Astonishing Behavior of Recursive Sequences, Quanta Magazine, Nov 16 2023, 13 pages.

Formula

Matsuhira, Matsusaka, & Tsuchida prove that a(n) >= 19. - Charles R Greathouse IV, Nov 17 2023

Crossrefs

Cf. A003504, A005166, A005167.

Sequence in context: A350141 A198593 A039526 * A288641 A141924 A122617

Adjacent sequences: A108391 A108392 A108393 * A108395 A108396 A108397

Keyword

nonn

Author

William Rex Marshall, Jul 02 2005

Status

approved