A363038 The decimal digits of a(n) correspond to the Gilbreath transform of the decimal digits of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 10, 11, 12, 13, 14, 15, 16, 17, 18, 22, 21, 20, 21, 22, 23, 24, 25, 26, 27, 33, 32, 31, 30, 31, 32, 33, 34, 35, 36, 44, 43, 42, 41, 40, 41, 42, 43, 44, 45, 55, 54, 53, 52, 51, 50, 51, 52, 53, 54, 66, 65, 64, 63, 62, 61, 60, 61

Offset: 0

Author

Rémy Sigrist, May 14 2023

Keywords

• nonn
• base
• easy

Comments

Leading zeros are ignored.

This sequence preserves the number of digits (A055642) as well as the initial digit (A000030).

Examples

			For n = 1029: the Gilbreath transform of (1 0 2 9) is (1 1 1 4), so a(1029) = 1114.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• N. J. A. Sloane, Maple code for Gilbreath transform and related arrays

Crossrefs

Cf. A000030, A055642, A334727 (base-2 analog).

Programs

Mathematica

A363038[n_]:=Module[{d=IntegerDigits[n]},FromDigits[Join[{First[d]},Table[First[d=Abs[Differences[d]]],Length[d]-1]]]];Array[A363038,200,0] (* Paolo Xausa, May 19 2023 *)

PARI

a(n, base = 10) = { my (d = digits(n, base), t = vector(#d)); for (i = 1, #d, t[i] = d[1]; d = vector(#d-1, j, abs(d[j+1]-d[j]));); fromdigits(t, base); }