A340138 a(1)=0, a(n+1) = the least m not already in the sequence such that the decimal digital root r of a(n-1) is found somewhere among the decimal digits of m.

0, 10, 1, 11, 2, 12, 3, 13, 4, 14, 5, 15, 6, 16, 7, 17, 8, 18, 9, 19, 21, 23, 25, 27, 29, 20, 22, 24, 26, 28, 31, 34, 37, 41, 35, 38, 32, 45, 39, 30, 33, 36, 49, 40, 42, 46, 51, 56, 52, 47, 62, 48, 43, 57, 53, 58, 44, 68, 50, 54, 59, 55, 61, 67, 64, 71, 78, 60

Offset

1,2

Comments

a(n) = 10^k occurs before n = 10^k for 0 < k <= 5.

Conjecture: permutation of the nonnegative numbers.

A decimal version of A339607, a permutation of the integers having to do with binary weight, but instead using digital root rather than digit sum. The plots of these sequences have similar features.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Plot (n, a(n)) for 1 <= n <= 10^3 with records in dark red and least unused numbers in dark blue, with records of a(n)-n in red, many labeled, and records of n-a(n) in blue, many labeled.

Michael De Vlieger, Logarithmic plot (n, a(n)-n) for 1 <= n <= 10^5 with records labeled in red, records of n-a(n) labeled in blue, and zeros plotted in black.

Mathematica

Block[{a = {0, 10}, k, r}, Do[k = 1; r = # + 9 Boole[# == 0] &@ Mod[a[[-1]], 9]; While[Nand[FreeQ[a, k], ! FreeQ[IntegerDigits[k], r]], k++]; AppendTo[a, k], 66]; a]

Crossrefs

Cf. A248025, A338191, A339607.

Sequence in context: A366013 A317330 A238880 * A332177 A130858 A098760

Adjacent sequences: A340135 A340136 A340137 * A340139 A340140 A340141

Keyword

nonn,base

Author

Michael De Vlieger, Jan 21 2021

Status

approved