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A113608
Apply the map k -> A040115(k) repeatedly to n until a single digit is reached.
1
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
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
KEYWORD
base,easy,nonn,changed
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