A005166 a(0) = 1; a(n) = (1 + a(0)^3 + ... + a(n-1)^3)/n (not always integral!). (Formerly M1551)

1, 2, 5, 45, 22815, 2375152056927, 2233176271342403475345148513527359103

Offset

0,2

Comments

Terms are integers until n=A097398(2,2)=89.

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

References

R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section E15.

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..9

R. K. Guy, Letter to N. J. A. Sloane, Sep 25 1986.

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.

Eric Weisstein's World of Mathematics, Goebel's Sequence.

Mathematica

a[0]=1; a[n_]:=(1 + Sum[a[k]^3, {k, 0, n-1}])/n; Array[a, 7, 0] (* Stefano Spezia, Oct 13 2024 *)

Crossrefs

Cf. A003504, A005167.

Cf. A108394.

Sequence in context: A334252 A307147 A056680 * A121621 A225147 A119715

Adjacent sequences: A005163 A005164 A005165 * A005167 A005168 A005169

Keyword

nonn,easy,nice,changed

Author

N. J. A. Sloane

Status

approved