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%I #23 Nov 17 2023 19:18:37
%S 43,89,97,214,19,239,37,79,83,239,31,431,19,79,23,827,43,173,31,103,
%T 94,73,19,243,141,101,53,811,47,1077,19,251,29,311,134,71,23,86,43,47,
%U 19,419,31,191,83,337,59,1559,19,127,109,163,67,353,83,191,83,107,19,503
%N Least k for which f(k) = (1 + f(0)^n + f(1)^n + ... + f(k-1)^n)/k, f(0) = 1, is nonintegral.
%D Ian Stewart, Professor Stewart's Hoard of Mathematical Treasures, "Life, Recursion and Everything", Basic Books, NY, 2009, p. 239-240.
%H R. K. Guy, <a href="/A005165/a005165.pdf">The strong law of small numbers</a>. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]
%H Rinnosuke Matsuhira, Toshiki Matsusaka, and Koki Tsuchida, <a href="https://arxiv.org/abs/2307.09741">How long can k-Göbel sequences remain integers?</a>, arXiv:2307.09741 [math.NT], 2023.
%H Alex Stone, <a href="https://www.quantamagazine.org/the-astonishing-behavior-of-recursive-sequences-20231116/">The Astonishing Behavior of Recursive Sequences</a>, Quanta Magazine, Nov 16 2023, 13 pages.
%F Matsuhira, Matsusaka, & Tsuchida prove that a(n) >= 19. - _Charles R Greathouse IV_, Nov 17 2023
%Y Cf. A003504, A005166, A005167.
%K nonn
%O 2,1
%A _William Rex Marshall_, Jul 02 2005
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