A322010 Inverse permutation to A322000.

0, 1, 2, 4, 6, 10, 14, 20, 26, 36, 3, 5, 7, 11, 15, 21, 27, 37, 46, 59, 8, 12, 16, 22, 28, 38, 47, 60, 72, 90, 17, 23, 29, 39, 48, 61, 73, 91, 108, 130, 30, 40, 49, 62, 74, 92, 109, 131, 152, 182, 50, 63, 75, 93, 110, 132, 153, 183, 212, 248, 76, 94, 111, 133, 154, 184, 213, 249

Offset

0,3

Comments

a(n) is the position of n in the list A322000 of "decibinary numbers", i.e., integers sorted according to their decibinary value A028897(n) = Sum d[i]*2^i, where d[i] are the decimal digits of n.

For 0 <= m <= 9, we have a(n) = A322003(n) = A000123(n-1), because 1..9 are the first few terms of A322000 where the decibinary value increases.

We see that a(10..19) = a(2..9)+1 concatenated with (46, 49). Then, a(20..29) = a(12..19)+1 concatenated with (72, 90). Then, a(30..39) = a(22..29)+1 concatenated with (108, 130), and so on. This yields an alternate way to compute the sequence.

Links

Table of n, a(n) for n=0..67.

Prog

(PARI) vec_A322010=vecsort(A, , 1)[1..vecmin(setminus([1..#A], Set(A)))-1] \\ Assumes the vector A = A322000(1..N) has been computed for some N. Exclude initial 0's to have correct (1-based) indices of the vectors.

Crossrefs

Cf. A322000, A028897, A322003, A072170(.,10), A000123.

Sequence in context: A333574 A008804 A001307 * A322003 A088932 A088954

Adjacent sequences: A322007 A322008 A322009 * A322011 A322012 A322013

Keyword

nonn

Author

M. F. Hasler, Feb 19 2019

Status

approved