

A114135


Primitive numbers n such that the sums of the digits of n, n^2 and n^3 coincide (cf. A111434).


4



1, 468, 585, 5851, 5868, 28845, 58968, 21688965, 29588877, 37848897, 49879981, 58577797, 79898994, 79958368, 79979698, 89757468, 109699677, 159699969, 468957888, 479597652, 479896587, 480749985, 494899398, 497349981, 498678256
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OFFSET

1,2


COMMENTS

Members of A111434 not congruent to 0 (mod 10). If k is a member of A111434 then so is 10^e*k.
The authors have calculated all members below 10^11.
The number of members less than 10^n {n=0..11}: 0,1,1,3,5,7,7,7,16,34,57,125.
Number of members congruent to k (mod 10): 0,7,1,0,2,23,8,20,49,15. But more interesting, number of members are congruent to k (mod 9): 66,59,0,0,0,0,0,0,0.
A007953(n) == n mod 9. Since 0 and 1 are the only k in [0,1,...8] with k == k^2 mod 9, all terms are congruent to 0 or 1 mod 9.  Robert Israel, Jan 26 2015


LINKS

Toshitaka Suzuki and Nikhil Mahajan, Table of n, a(n) for n = 1..600 (first 325 terms from Toshitaka Suzuki)


MATHEMATICA

sod[n_] := Plus @@ IntegerDigits@n; lst = {}; Do[ If[(Mod[n, 9] == 0  Mod[n, 9] == 1) && Mod[n, 10] != 0 && sod@n == sod[n2] == sod[n3], AppendTo[lst, n]], {n, 108/2}]; lst


PROG

(PARI) isok(n) = (n % 10) && ((sd=sumdigits(n)) == sumdigits(n^2)) && (sd == sumdigits(n^3)); \\ Michel Marcus, Jan 20 2015


CROSSREFS

Cf. A007953, A111434, A005188.
Sequence in context: A036340 A059395 A221238 * A043364 A054756 A205415
Adjacent sequences: A114132 A114133 A114134 * A114136 A114137 A114138


KEYWORD

base,nonn


AUTHOR

Giovanni Resta and Robert G. Wilson v, Nov 21 2005


STATUS

approved



