A114135 Primitive numbers n such that the sums of the digits of n, n^2 and n^3 coincide (cf. A111434).

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

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
Select[Range[5*10^8], Length[Union[Total/@IntegerDigits/@{#, #^2, #^3}]]==1 && Mod[#, 10]!=0&] (* Harvey P. Dale, Jul 07 2020 *)

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: A059395 A266163 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