A113608 Apply the map k -> A040115(k) repeatedly to n until a single digit is reached.

1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 1

Offset

10,4

Comments

Leading zeros at any intermediate result are discarded. The first terms, from n=10 to n=99, are identical to A040115. - R. J. Mathar, Aug 28 2007

Links

T. D. Noe, Table of n, a(n) for n=10..10000

Example

a(1396) = 1 because A040115(1396) = 263, A040115(263) = 43, A040115(43) = 1.
a(1237584965) = 1 from 6-fold application of A040115: 1237584965 -> 114234531 -> 3211122 -> 110010 -> 01011 = 1011 -> 110 -> 01 -> 1.

Maple

A040115 := proc(n) local digs, digsdiff, i; digsdiff := [] ; digs := convert(n, base, 10) ; for i from 2 to nops(digs) do digsdiff := [op(digsdiff), abs(op(i, digs)-op(i-1, digs))] ; od; add( op(i, digsdiff)*10^(i-1), i=1..nops(digsdiff)) ; end:
A113608 := proc(n) local a; a := A040115(n) ; while a>9 do a := A040115(a) ; od; RETURN(a) ; end: seq(A113608(n), n=10..110) ; # R. J. Mathar, Aug 28 2007

Mathematica

a[n_] := NestWhile[FromDigits[Abs[Differences[IntegerDigits[#]]]] &, n, # > 9 &]; Array[a, 120, 10] (* Amiram Eldar, Nov 12 2024 *)

Crossrefs

Cf. A040115.

Sequence in context: A040114 A064834 A040163 * A040115 A080465 A347689

Adjacent sequences: A113605 A113606 A113607 * A113609 A113610 A113611

Keyword

base,easy,nonn

Author

Amarnath Murthy, Nov 09 2005

Extensions

Edited and extended by R. J. Mathar, Aug 28 2007

Further edited by N. J. A. Sloane, Aug 19 2008

Status

approved