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Search: id:A113608
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| A113608 |
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Apply the map k -> A040115(k) repeatedly to n until a single digit is reached. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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10,4
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COMMENT
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Leading zeros at any intermediate result are discarded. The first terms, from n=10 to n=99, are identical to A040115. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 28 2007
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EXAMPLE
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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.
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MAPLE
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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 (mathar(AT)strw.leidenuniv.nl), Aug 28 2007
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CROSSREFS
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Cf. A040115.
Sequence in context: A040114 A064834 A040163 this_sequence A040115 A080465 A113607
Adjacent sequences: A113605 A113606 A113607 this_sequence A113609 A113610 A113611
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KEYWORD
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base,easy,nonn,new
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 09 2005
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 28 2007
Further edited by njas, Aug 19 2008
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