A254621 Zerofree numbers having product of digits less than or equal to sum of digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 31, 41, 51, 61, 71, 81, 91, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 122, 123, 131, 132, 141, 151, 161, 171, 181, 191, 211, 212, 213, 221, 231, 311, 312, 321, 411

Offset

1,2

Comments

Intersection of A052382 and A062996.

The repunit A002275(k), for k >= 2, appears at position A254622(k-1) + 1. - Wolfdieter Lang, Feb 23 2015

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Maple

extend:= proc(t, b, d)
  local i, j, m, s, p;
  p:= t[2];
  s:= t[3];
  if s = 0  then if b=2 then j:= 3 else j:= 2 fi
  else  for j from 0 to d-nops(t[1]) while p*b^j <= s + j*b do od
  fi:
  seq([[op(t[1]), b$i], p*b^i, s+i*b], i=0..j-1);
end proc:
f:= proc(d)
   local j, b, Res;
   Res:= [seq([[1$j], 1, j], j=0..d)];
   for b from 2 to 9 do
     Res:= map(extend, Res, b, d)
   od:
   Res:= map(t -> op(combinat:-permute(t[1])), Res);
   subs(0=NULL, sort(map(t -> add(t[i]*10^(i-1), i=1..nops(t)), Res)));
end proc:
f(5); # Robert Israel, May 19 2015

Mathematica

m[w_] := Flatten@Table[i, {i, 9}, {w[[i]]}]; a[upd_] := Union@ Flatten@ Table[ FromDigits /@ Flatten[Permutations /@ m /@ Select[ Flatten[ Permutations /@ (IntegerPartitions[d + 9, {9}, Range[d + 1]] - 1), 1], Times @@ (Range[9]^#) <= Total[# Range[9]] &], 1], {d,  upd}]; a[12] (* terms with up to 12 digits, Giovanni Resta, May 19 2015 *)
zfnQ[n_]:=Module[{idn=IntegerDigits[n]}, FreeQ[idn, 0]&&Times@@idn <= Total[ idn]]; Select[Range[500], zfnQ] (* Harvey P. Dale, Jun 29 2019 *)

Prog

(PARI) is(n)={my(d=digits(n)); my(p=prod(i=1, #d, d[i])); 0 < p && p<=vecsum(d) } \\ David A. Corneth, May 15 2015

Crossrefs

Cf. A052382, A062996, A062997, A062998, A062999, A254622, A002275.

Sequence in context: A277061 A361978 A090274 * A227510 A032898 A131058

Adjacent sequences: A254618 A254619 A254620 * A254622 A254623 A254624

Keyword

nonn,base

Author

David A. Corneth, Feb 03 2015

Status

approved