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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.

%I A342978 #27 Mar 19 2025 15:29:40
%S A342978 1,2,3,4,5,6,7,8,9,99,89,79,69,59,49,98,999,88,899,78,799,68,699,39,
%T A342978 58,599,48,9999,989,97,499,998,8999,889,87,898,789,7999,77,38,798,689,
%U A342978 67,6999,29,698,57,589,399,5999,598,47,99999,9899,489,9989,4999,9998
%N 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.
%H A342978 David A. Corneth, <a href="/A342978/b342978.txt">Table of n, a(n) for n = 1..10000</a>
%H A342978 David A. Corneth, <a href="/A342978/a342978.gp.txt">PARI program</a>
%e A342978 For k=1 to 9, k/A007954(k) = 1, the least possible value, so a(k)=k for k=1 to 9.
%e A342978 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.
%o A342978 (PARI) \\ up to d digits
%o A342978 nonzero(n) = vecmin(digits(n));
%o A342978 pd(n) = n/vecprod(digits(n));
%o A342978 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);}
%o A342978 (PARI) \\ See Corneth link. _David A. Corneth_, Apr 02 2021
%Y A342978 Cf. A007954 (product of decimal digits), A052382 (zeroless numbers).
%K A342978 nonn,look,base
%O A342978 1,2
%A A342978 _Michel Marcus_, Apr 02 2021