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A088359
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Numbers which occur only once in A004001.
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28
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3, 5, 6, 9, 10, 11, 13, 17, 18, 19, 20, 22, 23, 25, 28, 33, 34, 35, 36, 37, 39, 40, 41, 43, 44, 46, 49, 50, 52, 55, 59, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 77, 78, 79, 81, 82, 84, 87, 88, 89, 91, 92, 94, 97, 98, 100, 103, 107, 108, 110, 113, 117, 122, 129, 130, 131, 132
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Out of the first one million terms (a(10^6) = 510403), 258661 occur only once.
In general, out of the first 2^(n+1) terms of A004001, 2^(n-1) - 1 terms (a quarter) occur only once. See also illustration in A265332.
One more than the positions of ones in A093879.
(End)
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LINKS
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FORMULA
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Other identities.
For all n >= 0, a(A000079(n)) = A000051(n+1), that is, a(2^n) = 2^(n+1) + 1.
For all n >= 1:
(End)
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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]]; hc = Table[ a[n], {n, 1, 261}]; RunLengthEncodeOne[x_List] := Length[ # ] == 1 & /@ Split[x]; r = RunLengthEncodeOne[hc]; Select[ Range[ Length[r]], r[[ # ]] == True &]
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PROG
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(Haskell)
import Data.List (elemIndices)
a088359 n = a088359_list !! (n-1)
a088359_list = map succ $ elemIndices 1 a051135_list
(Scheme, with Antti Karttunen's IntSeq-library)
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CROSSREFS
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Cf. A188163 (same sequence with prepended 1).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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