A005167 a(n+1) = (1 + a(0)^4 + ... + a(n)^4 )/(n+1) (not always integral!). (Formerly M1957)

1, 2, 9, 2193, 5782218987645, 223567225753623833253893162919867828939456664850241

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

T. D. Noe, Table of n, a(n) for n=0..7

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]

N. Lygeros & M. Mizony, Study of primality of terms of a_k(n)=(1+(sum from 1 to n-1)(a_k(i)^k))/(n-1) [dead link]

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. A005166, A003504.

Cf. A108394.

Sequence in context: A221177 A181865 A271081 * A208213 A067039 A208214

Adjacent sequences: A005164 A005165 A005166 * A005168 A005169 A005170

Keyword

easy,nonn,nice

Author

N. J. A. Sloane

Status

approved