A338834 a(n) is the greatest number not yet in the sequence with the same number of digits and the same sum of digits as n in factorial base.

0, 1, 2, 4, 3, 5, 6, 12, 8, 18, 14, 20, 7, 13, 10, 19, 16, 22, 9, 15, 11, 21, 17, 23, 24, 48, 30, 72, 54, 96, 26, 50, 49, 78, 74, 102, 36, 73, 60, 98, 97, 108, 56, 84, 80, 104, 103, 114, 25, 32, 31, 55, 52, 79, 28, 51, 42, 76, 75, 100, 38, 66, 62, 99, 90, 110

Offset: 0

Author

Rémy Sigrist, Nov 11 2020

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

Examples

			For n = 26:
- the numbers with 4 digits and sum of digits 2 in factorial base are: 25 ("1001"), 26 ("1010"), 30 ("1100") and 48 ("2000"),
- so a(25) = 40,
     a(26) = 30,
     a(30) = 26,
     a(40) = 25.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..5039
• Rémy Sigrist, Colored scatterplot of the first 7! terms (where the color is function of A034968(n))
• Rémy Sigrist, PARI program for A338834
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A034968, A084558, A337598, A338829 (decimal analog), A338835 (primorial base analog).

Programs

PARI

See Links section.

Formula

A084558(a(n)) = A084558(n).

A034968(a(n)) = A034968(n).