A342978 Zeroless numbers k ordered according to k/A007954(k), and in case of ties by k, where A007954(k) is the product of digits of k.

1, 2, 3, 4, 5, 6, 7, 8, 9, 99, 89, 79, 69, 59, 49, 98, 999, 88, 899, 78, 799, 68, 699, 39, 58, 599, 48, 9999, 989, 97, 499, 998, 8999, 889, 87, 898, 789, 7999, 77, 38, 798, 689, 67, 6999, 29, 698, 57, 589, 399, 5999, 598, 47, 99999, 9899, 489, 9989, 4999, 9998

Offset: 1

Author

Michel Marcus, Apr 02 2021

Keywords

• nonn
• look
• base

Examples

			For k=1 to 9, k/A007954(k) = 1, the least possible value, so a(k)=k for k=1 to 9.
Then we have 99, 89, 79, 69, 59, 49, 98 with 1.22, 1.23, 1.25, 1.27, 1.31, 1.36, 1.36.
		

Links

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

Crossrefs

Cf. A007954 (product of decimal digits), A052382 (zeroless numbers).

Programs

PARI

\\ up to d digits
nonzero(n) = vecmin(digits(n));
pd(n) = n/vecprod(digits(n));
lista(d) = {my(lim = 10^d-1, vk = select(nonzero, [1..lim]), vpk = vector(#vk, k, pd(vk[k])), vsk = vecsort(vpk, ,1)); my(vall = vector(#vsk, k, vk[vsk[k]])); my(out = List(), k = 1); while(vall[k] != lim, listput(out, vall[k]); k++); listput(out, vall[k]); Vec(out);}

PARI

\\ See Corneth link. David A. Corneth, Apr 02 2021