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

0,3

Comments

Leading zeros are ignored.

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

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

N. J. A. Sloane, Maple code for Gilbreath transform and related arrays

Example

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

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 *)

Prog

(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); }

Crossrefs

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

Sequence in context: A261333 A330430 A031086 * A127288 A127287 A239088

Adjacent sequences: A363035 A363036 A363037 * A363039 A363040 A363041

Keyword

nonn,base,easy

Author

Rémy Sigrist, May 14 2023

Status

approved