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A005167 a(n+1) = (1 + a(0)^4 + ... + a(n)^4 )/(n+1) (not always integral!).
(Formerly M1957)
6
1, 2, 9, 2193, 5782218987645, 223567225753623833253893162919867828939456664850241 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Terms are integer until n=A097398(3,2)=97.
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
The next term -- a(6) -- has 201 digits. - Harvey P. Dale, Nov 20 2018
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712.
R. K. Guy, The strong law of small numbers. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]
Alex Stone, The Astonishing Behavior of Recursive Sequences, Quanta Magazine, Nov 16 2023, 13 pages.
MATHEMATICA
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 *)
CROSSREFS
Cf. A108394.
Sequence in context: A221177 A181865 A271081 * A208213 A067039 A208214
KEYWORD
easy,nonn,nice
AUTHOR
STATUS
approved

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Last modified April 25 11:06 EDT 2024. Contains 371967 sequences. (Running on oeis4.)