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A067109
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Number of occurrences of the string n in n! (A000142).
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3
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1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 0, 2, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 2, 4, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 5, 0
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OFFSET
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1,37
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COMMENTS
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LINKS
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EXAMPLE
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a(4) = 1 as 4! = 24 and 4 occurs once;
a(5) = 0 as 5! = 120 does not contain a 5;
a(20) = 1 as 20! = 2432902008176640000 and 20 occurs once.
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MATHEMATICA
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Table[ Length[ StringPosition[ ToString[n! ], ToString[n]]], {n, 1, 75} ]
Table[SequenceCount[IntegerDigits[n!], IntegerDigits[n], Overlaps->True], {n, 100}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 01 2019 *)
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PROG
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(Haskell)
import Data.List (tails, isPrefixOf)
a067109 n = sum $
map (fromEnum . (show n `isPrefixOf`)) (tails $ show $ a000142 n)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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