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%I M1551 #37 Nov 17 2023 19:17:20
%S 1,2,5,45,22815,2375152056927,2233176271342403475345148513527359103
%N a(0) = 1; a(n) = (1 + a(0)^3 + ... + a(n-1)^3)/n (not always integral!).
%C Terms are integers until n=A097398(2,2)=89.
%C Guy states that by computing the sequence modulo 89 it is easy to show that a(89) is not integral. - _T. D. Noe_, Sep 17 2007
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A005166/b005166.txt">Table of n, a(n) for n=0..9</a>
%H R. K. Guy, <a href="/A005169/a005169_6.pdf">Letter to N. J. A. Sloane</a>, Sep 25 1986.
%H R. K. Guy, <a href="http://www.jstor.org/stable/2322249">The strong law of small numbers</a>. Amer. Math. Monthly 95 (1988), no. 8, 697-712.
%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 N. Lygeros & M. Mizony, <a href="http://igd.univ-lyon1.fr/home/mizony/premiers.html">Study of primality of terms of a_k(n)=(1+(sum from 1 to n-1)(a_k(i)^k))/(n-1)</a> [dead link]
%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.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoebelsSequence.html">Goebel's Sequence.</a>
%Y Cf. A003504, A005167.
%Y Cf. A108394.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_
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