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A039997
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Number of distinct primes which occur as substrings of the digits of n.
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10
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0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 2, 0, 1, 0, 2, 0, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 3, 1, 1, 0, 1, 1, 2, 0, 1, 0, 2, 0, 0, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 2, 2, 3, 1, 2, 1, 1, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 1, 1, 2, 0, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,13
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COMMENTS
| a(A062115(n))=0; a(A093301(n))=n and a(m)<>n for m < A093301(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 16 2007
a(A163753(n)) > 0; a(A205667(n)) = 1. [Reinhard Zumkeller, Jan 31 2012]
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000
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EXAMPLE
| a(22)=1 because 22 has two substrings which are prime but they are identical. a(103)=2, since the primes 3 and 103 occur as substrings.
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MATHEMATICA
| a[n_] := Block[{s = IntegerDigits[n], c = 0, d = {}}, l = Length[s]; t = Flatten[ Table[ Take[s, {i, j}], {i, 1, l}, {j, i, l}], 1]; k = l(l + 1)/2; While[k > 0, If[ t[[k]][[1]] != 0, d = Append[d, FromDigits[ t[[k]] ]]]; k-- ]; Count[ PrimeQ[ Union[d]], True]]; Table[ a[n], {n, 1, 105}]
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PROG
| (Haskell)
import Data.List (isInfixOf)
a039997 n = length [p | p <- takeWhile (<= n) a000040_list,
show p `isInfixOf` show n]
a039997_list = map a039997 [1..]
-- Reinhard Zumkeller, Jan 31 2012
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CROSSREFS
| Different from A039995 after the 100th term. Cf. A035232.
Sequence in context: A113686 A192033 A193403 * A039995 A035232 A091603
Adjacent sequences: A039994 A039995 A039996 * A039998 A039999 A040000
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KEYWORD
| nonn,base
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AUTHOR
| Dave Wilson
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 24 2003
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