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A257760 Zeroless numbers n such that the products of the decimal digits of n and n^2 coincide. 4

%I

%S 1,1488,3381,14889,18489,181965,262989,338646,358489,367589,437189,

%T 438329,479285,781839,964941,1456589,1763954,2579285,2868489,3365285,

%U 3419389,3451988,3584889,3625619,4378829,4653989,6868877,7295986,9548479,14529839,14534488

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

%C It is unknown if this sequence is infinite.

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

%C 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

%H Robert G. Wilson v, <a href="/A257760/b257760.txt">Table of n, a(n) for n = 1..1747</a> (first 75 terms from Pieter Post)

%e 1488 is in the sequence since 1488^2 = 2214144 and we have 256 = 1*4*8*8 = 2*2*1*4*1*4*4.

%e 3381 is in the sequence because 3381^2 = 11431161 and 72 = 3*3*8*1 = 1*1*4*3*1*1*6*1.

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

%o (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

%Y Subsequence of A052040.

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

%K nonn,base

%O 1,2

%A _Pieter Post_, May 07 2015

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Last modified May 7 14:09 EDT 2021. Contains 343650 sequences. (Running on oeis4.)