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

Author

Amarnath Murthy, Nov 09 2005

Keywords

• base
• easy
• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A040115.

Programs

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 *)

Extensions

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

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