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 A006887 Kaprekar triples: q such that q = x + y + z and q^3 = x*10^2n + y*10^n + z, where z < 10^n and n is the number of digits in q. q is not a power of 10 (except q=1). (Formerly M4478) 9
 1, 8, 45, 297, 2322, 2728, 4445, 4544, 4949, 5049, 5455, 5554, 7172, 27100, 44443, 55556, 60434, 77778, 143857, 208494, 226071, 279720, 313390, 324675, 329967, 346060, 368928, 395604, 422577, 427868, 461539, 472823, 478115, 488214, 494208 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A291461. Sequence in context: A055422 A204618 A289896 * A009369 A120044 A328885 Adjacent sequences: A006884 A006885 A006886 * A006888 A006889 A006890 KEYWORD nonn,base AUTHOR Robert Munafo EXTENSIONS Entry revised by Larry Reeves (larryr(AT)acm.org), Apr 25 2001 and Dec 08 2002 STATUS approved

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Last modified May 28 07:31 EDT 2023. Contains 362992 sequences. (Running on oeis4.)