A005167 - OEIS

%I M1957 #32 Nov 17 2023 19:18:02

%S 1,2,9,2193,5782218987645,

%T 223567225753623833253893162919867828939456664850241

%N a(n+1) = (1 + a(0)^4 + ... + a(n)^4 )/(n+1) (not always integral!).

%C Terms are integer until n=A097398(3,2)=97.

%C Guy states that by computing the sequence modulo 97 it is easy to show that a(97) is not integral. - _T. D. Noe_, Sep 17 2007

%C The next term -- a(6) -- has 201 digits. - _Harvey P. Dale_, Nov 20 2018

%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="/A005167/b005167.txt">Table of n, a(n) for n=0..7</a>

%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.

%t nxt[{n_,a_,t_}]:={n+1,(1+t)/(n+1),t+((1+t)/(n+1))^4}; NestList[nxt,{0,1,1},5][[All,2]] (* _Harvey P. Dale_, Nov 20 2018 *)

%Y Cf. A005166, A003504.

%Y Cf. A108394.

%K easy,nonn,nice

%O 0,2

%A _N. J. A. Sloane_