OFFSET
1,2
COMMENTS
The initial term a(1) = 1 is somewhat conventional: it is the only term with x = y = 0 and q = z = 10^k, which is explicitly allowed only for k = 0 and forbidden for k > 0. In all other cases, 0 < x, y, z < q, and q^3 has the same number of digits as x*10^2n. - M. F. Hasler, Aug 24 2017
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, NY, 1986, p. 151.
LINKS
Jack Brennen and Hans Havermann, Table of n, a(n) for n = 1..1000 (first 200 terms from Giovanni Resta)
Futility Closet's "Math Notes", Shows the cubes of a(9) to a(13)
Hans Havermann, Cube wonders
Douglas E. Iannucci and Bertrum Foster, Kaprekar Triples, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.8.
R. Munafo, Kaprekar Sequences
EXAMPLE
1 = 0 + 0 + 1 and 1^3 = (00)1 (cf. comment),
8 = 5 + 1 + 2 and 8^3 = 512,
45 = 9 + 11 + 25, and 45^3 = 91125. - M. F. Hasler, Aug 24 2017
MATHEMATICA
ok[n_] := n==1 || Block[{k = 10^IntegerLength[n], m = n^3}, n == Mod[m, k] + Floor[ m/k^2] + Mod[Floor[m/k], k] && ! IntegerQ@ Log10@ n]; Select[ Range@ 500000, ok] (* Giovanni Resta, Aug 23 2017 *)
PROG
(PARI) m=1; for(n=1, 6, for(q=m+(n>1), -1+m*=10, q==sumdigits(q^3, m)&&print1(q", "))) \\ M. F. Hasler, Aug 24 2017
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
Entry revised by Larry Reeves (larryr(AT)acm.org), Apr 25 2001 and Dec 08 2002
STATUS
approved