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A051135
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a(n) = number of times n appears in the Hofstadter-Conway $10000 sequence A004001.
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8
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2, 2, 1, 3, 1, 1, 2, 4, 1, 1, 1, 2, 1, 2, 3, 5, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 6, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 7, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 3, 1, 2, 3
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OFFSET
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1,1
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COMMENTS
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If the initial 2 is changed to a 1, the resulting sequence has the property that if all 1's are deleted, the remaining terms are the sequence incremented. - Franklin T. Adams-Watters, Oct 05 2006
a(A088359(n))=1 and a(A087686(n))>1; first differences of A188163. [Reinhard Zumkeller, Jun 03 2011]
Start:
a(k)=1 for k= 3, 5, 6, 9, 10, 11, 13, 17, 18, 19, 20, 22, 23, 25, 28, ..., ;
a(k)=2 for k= 1, 2, 7, 12, 14, 21, 24, 26, 29, 38, 42, 45, 47, 51, 53, ..., ;
a(k)=3 for k= 4, 15, 27, 30, 48, 54, 57, 61, 86, 96, 102, 105, 112, ..., ;
a(k)=4 for k= 8, 31, 58, 62, 106, 116, 120, 125, 192, 212, 222, 226, ..., ;
a(k)=5 for k= 16, 63, 121, 126, 227, 242, 247, 253, 419, 454, 469, ..., ;
a(k)=6 for k= 32, 127, 248, 254, 475, 496, 502, 509, 894, 950, 971, ..., ;
a(k)=7 for k= 64, 255, 503, 510, 978, 1006, 1013, 1021, 1872, 1956, ..., ;
a(k)=8 for k= 128, 511, 1014, 1022, 1992, 2028, 2036, 2045, 3864, ..., ;
a(k)=9 for k= 256, 1023, 2037, 2046, 4029, 4074, 4083, 4093, 7893, ..., ;
a(k)=10 for k= 512, 2047, 4084, 4094, 8113, 8168, 8178, 8189, ..., ; etc. Robert G. Wilson v, June 7 2011.
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000
Wikipedia, Hofstadter sequence
Eric Weisstein's World of Mathematics, Hofstadter-Conway $10,000 Sequence.
Index entries for Hofstadter-type sequences
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MAPLE
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a[1]:=1: a[2]:=1: for n from 3 to 300 do a[n]:=a[a[n-1]]+a[n-a[n-1]] od: A:=[seq(a[n], n=1..300)]:for j from 1 to A[nops(A)-1] do c[j]:=0: for n from 1 to 300 do if A[n]=j then c[j]:=c[j]+1 else fi od: od: seq(c[j], j=1..A[nops(A)-1]); - Emeric Deutsch, Jun 06 2006
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MATHEMATICA
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a[1] = 1; a[2] = 1; a[n_] := a[n] = a[a[n - 1]] + a[n - a[n - 1]]; t = Array[a, 250]; Take[ Transpose[ Tally[t]][[2]], 105] (* Robert G. Wilson v, June 7 2011 *)
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PROG
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(Haskell)
import Data.List (group)
a051135 n = a051135_list !! (n-1)
a051135_list = map length $ group a004001_list
-- Reinhard Zumkeller, Jun 03 2011
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CROSSREFS
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Cf. A004001, A088359.
Sequence in context: A116687 A056044 A116685 * A135352 A072528 A166363
Adjacent sequences: A051132 A051133 A051134 * A051136 A051137 A051138
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KEYWORD
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easy,nonn,nice
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AUTHOR
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Robert Lozyniak (11(AT)onna.com)
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EXTENSIONS
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More terms from Jud McCranie
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STATUS
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approved
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