cp's OEIS Frontend

A274126 Numbers with digits larger than 1 sorted by product of digits minus sum of digits, then by size.

%I A274126 #36 Jan 05 2021 21:41:34
%S A274126 2,3,4,5,6,7,8,9,22,23,24,222,25,33,26,27,34,223,28,29,35,44,224,2222,
%T A274126 36,233,37,45,225,38,46,226,39,55,234,2223,47,227,333,56,48,228,235,
%U A274126 244,2224,22222,49,57,229,66,236,334,2233,58,67,245,2225,237,59,68,335
%N A274126 Numbers with digits larger than 1 sorted by product of digits minus sum of digits, then by size.
%C A274126 Let PS(n) be product of digits of n minus sum of digits of n (=-A062329(n)). Then a(n) is PS(A037344(m)) ordered by PS(n) for values of m such that A037344 has its digits in nondecreasing order. If PS(m) some nonzero term m of A002276 exceed some bound, all positive integers t larger than that term without zeros and ones exceed have a larger value for PS(t).
%C A274126 Prepending -A062329(a(n)) or more ones before a(n) gives terms of A274125.
%C A274126 Permuting digits of A274125 gives A254621. Permutations of digits can be found in A261370. The union of A254621 and A011540 is A062996. The b-file lists terms having PS(n) <= 10^6.
%H A274126 David A. Corneth, <a href="/A274126/b274126.txt">Table of n, a(n) for n = 1..10696</a>
%H A274126 David A. Corneth, <a href="/A274126/a274126.gp.txt">PARI program</a>
%e A274126 Suppose we want to order the nondecreasing integers without zeros and ones up to PS(m) = 50. We see that 222222 has PS(222222) = 52, so we only have to check such nondecreasing integers up to 222222. Not all of those must be checked, which is used in the program.
%e A274126 25 is a term. Prepending PS(25) = -A062329(25) = 3 ones before 25 gives 11125, which is a term of A274125. Permuting digits of 11125 gives for example 12511, which is a term of A254621.
%o A274126 (PARI) See program in link "PARI program".
%Y A274126 Cf. A011540, A037344, A062329, A062996, A254621, A261370, A274125.
%K A274126 nonn,base
%O A274126 1,1
%A A274126 _David A. Corneth_, Jun 10 2016