A274125 -id:A274125 - cp's OEIS frontend

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

2, 3, 4, 5, 6, 7, 8, 9, 22, 23, 24, 222, 25, 33, 26, 27, 34, 223, 28, 29, 35, 44, 224, 2222, 36, 233, 37, 45, 225, 38, 46, 226, 39, 55, 234, 2223, 47, 227, 333, 56, 48, 228, 235, 244, 2224, 22222, 49, 57, 229, 66, 236, 334, 2233, 58, 67, 245, 2225, 237, 59, 68, 335

Offset: 1

David A. Corneth, Jun 10 2016

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).
Prepending -A062329(a(n)) or more ones before a(n) gives terms of A274125.
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.

			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.
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.

David A. Corneth, Table of n, a(n) for n = 1..10696
David A. Corneth, PARI program

Cf. A011540, A037344, A062329, A062996, A254621, A261370, A274125.

PARI
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See program in link "PARI program".
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cp's OEIS Frontend

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

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