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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)
6
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).

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 151.

LINKS

Jack Brennen and Hans Havermann, Table of n, a(n) for n = 1..780 (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 A002686

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 September 25 14:50 EDT 2017. Contains 292488 sequences.