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

1,1

Comments

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.

Links

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

David A. Corneth, PARI program

Example

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.

Prog

(PARI) See program in link "PARI program".

Crossrefs

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

Sequence in context: A249443 A299690 A318276 * A108194 A083158 A254956

Adjacent sequences: A274123 A274124 A274125 * A274127 A274128 A274129

Keyword

nonn,base

Author

David A. Corneth, Jun 10 2016

Status

approved