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

1, 2, 9, 2193, 5782218987645, 223567225753623833253893162919867828939456664850241

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn
• nice

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.

Crossrefs

Cf. A005166, A003504.

Cf. A108394.

Programs

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 *)