A064003 Numbers whose product of decimal digits equals its sum of binary digits.

1, 12, 13, 114, 115, 123, 131, 141, 151, 212, 231, 1122, 1611, 1911, 2121, 3211, 3311, 11124, 11215, 11251, 11421, 12114, 12311, 12411, 13121, 14121, 14211, 15211, 21114, 21212, 21221, 21411, 22121, 22211, 26111, 52111, 111118, 111119, 111133, 111142, 111241

Offset

1,2

Comments

The number of terms with d digits, for d = 1,...,20 is 1, 2, 8, 6, 19, 37, 49, 95, 152, 240, 374, 528, 748, 1174, 1607, 2415, 3309, 4687, 7202, 9357. - Giovanni Resta, Mar 28 2013

Links

Harry J. Smith and Donovan Johnson, Table of n, a(n) for n = 1..1000 (first 200 terms from Harry J. Smith)

Formula

{ k : A000120(k) = A007954(k) }.

Example

Product of digits of 15211 is 10, 15211 = 11101101101011 in binary with 10 "1's", hence 15211 is in the sequence.

Mathematica

Select[Range[120000], Times@@IntegerDigits[#]==Total[ IntegerDigits[#, 2]]&] (* Harvey P. Dale, Mar 01 2012 *)
(* dig[x] generates all terms with x digits *) dig[nd_] := Block[{dec, w}, dec[p_, n_] := If[Length@p == nd, n==1 && AppendTo[w, p], Do[If[Mod[n, x] == 0, dec[Append[p, x], n/x]], {x, Max[Max@p, 1], 9}]]; Sort@Flatten@Table[w = {}; dec[{}, nb]; Select[FromDigits /@ Flatten[Permutations /@ w, 1], Total@ IntegerDigits[#, 2] == nb &], {nb, Ceiling@Log[2, 10^nd]}]]; (* Giovanni Resta, Mar 28 2013 *)

Prog

(PARI) isok(k) = { vecprod(digits(k)) == hammingweight(k) } \\ Harry J. Smith, Sep 05 2009

Crossrefs

Subsequence of A052382.

Sequence in context: A041306 A058952 A058950 * A135123 A129476 A243361

Adjacent sequences: A064000 A064001 A064002 * A064004 A064005 A064006

Keyword

nonn,base

Author

Benoit Cloitre, Jun 05 2002

Status

approved