A354469 Write n in primorial base, then replace each nonzero digit d of radix p with p-d.

0, 1, 4, 5, 2, 3, 24, 25, 28, 29, 26, 27, 18, 19, 22, 23, 20, 21, 12, 13, 16, 17, 14, 15, 6, 7, 10, 11, 8, 9, 180, 181, 184, 185, 182, 183, 204, 205, 208, 209, 206, 207, 198, 199, 202, 203, 200, 201, 192, 193, 196, 197, 194, 195, 186, 187, 190, 191, 188, 189

Offset: 0

Author

Rémy Sigrist, Jun 02 2022

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers, similar to A225901.

There are exactly two fixed points: a(0) = 0 and a(1) = 1.

Examples

			For n = 42:
- the primorial base expansion of 42 is: (1, 2, 0, 0),
- the corresponding radixes are: (7, 5, 3, 2),
- so the primorial base expansion of a(42) is: (7-1, 5-2, 0, 0) = (6, 3, 0, 0),
- and a(42) = 198.
		

Links

• Index entries for sequences related to primorial base
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A225901, A235168.

Programs

PARI

a(n, s=i->prime(i)) = { my (v=0, f=1, r); for (i=1, oo, if (n==0, return (v), r=s(i); v+=f*((-n)%r); f*=r; n\=r)) }