A257760 Zeroless numbers n such that the products of the decimal digits of n and n^2 coincide.

1, 1488, 3381, 14889, 18489, 181965, 262989, 338646, 358489, 367589, 437189, 438329, 479285, 781839, 964941, 1456589, 1763954, 2579285, 2868489, 3365285, 3419389, 3451988, 3584889, 3625619, 4378829, 4653989, 6868877, 7295986, 9548479, 14529839, 14534488

Offset: 1

Author

Pieter Post, May 07 2015

Keywords

• nonn
• base

Comments

It is unknown if this sequence is infinite.

Number of terms < 10^n: 1, 1, 1, 3, 5, 15, 29, 75, 211, 583, 1694, ..., . - Robert G. Wilson v, May 25 2015

Also nontrivial numbers n such that the products of the decimal digits of n and n^2 are equal. Trivial solutions are any number which contains a zero in its decimal expansion. - Robert G. Wilson v, May 11 2015

Examples

			1488 is in the sequence since 1488^2 = 2214144 and we have 256 = 1*4*8*8 = 2*2*1*4*1*4*4.
3381 is in the sequence because 3381^2 = 11431161 and 72 = 3*3*8*1 = 1*1*4*3*1*1*6*1.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1747 (first 75 terms from Pieter Post)

Crossrefs

Subsequence of A052040.

Cf. A000290, A007954, A029793, A052382, A257763.

Programs

Mathematica

fQ[n_] := Times @@ IntegerDigits[n] == Times @@ IntegerDigits[n^2] > 0; Select[ Range@ 10000000, fQ] (* Robert G. Wilson v, May 07 2015 *)

PARI

isok(n) = (d = digits(n)) && vecmin(d) && (dd = digits(n^2)) && (prod(k=1, #d, d[k]) == prod(k=1, #dd, dd[k])); \\ Michel Marcus, May 07 2015