A318276 Numbers with digits in nondecreasing order without digit 1 whose multiplicative digital root is not 0.

2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 24, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 46, 47, 48, 49, 57, 66, 67, 68, 77, 79, 88, 89, 99, 222, 223, 224, 226, 227, 228, 229, 233, 234, 236, 237, 238, 244, 246, 248, 249, 266, 267, 277, 278, 279, 288, 289, 299, 333, 334

Offset: 1

Author

David A. Corneth, Aug 23 2018

Keywords

• nonn
• base
• look
• fini

Comments

This sequence is a primitive sequence of A299690 because terms of that sequence can be found using this; permuting digits of terms of this sequence gives terms in A299690.

This sequence is also a primitive sequence to A318275 as prepending 0 or more ones to terms in this sequence gives terms in A318275.

This sequence is finite because it's a subsequence of the finite sequence A299690.

Links

• David A. Corneth, Table of n, a(n) for n = 1..12413

Crossrefs

Cf. A299690, A318275.

Programs

Mathematica

Select[Range[333], And[FreeQ[IntegerDigits@ #, 1], FixedPoint[Times @@ IntegerDigits@ # &, #] != 0, AllTrue[Differences@ IntegerDigits@ #, # >= 0 &]] &] (* Michael De Vlieger, Aug 25 2018 *)

PARI

mdr(n)=n = fromdigits(n); while(n>9, n=factorback(digits(n))); n \\ from Charles R Greathouse IV at A299690.
uptoQdigits(n) = {my(res = List()); for(i = 1, n, forvec(x = vector(i, j, [2, 9]), c = mdr(x); if(c != 0, listput(res, fromdigits(x))), 1)); res} \\ David A. Corneth, Dec 31 2018

Extensions

Data corrected by David A. Corneth, Dec 31 2018