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A039995
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Number of distinct primes which occur as subsequences of the sequence of digits of n.
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6
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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, 2, 1, 3, 0, 1
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OFFSET
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1,13
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COMMENTS
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a(n) counts subsequences of digits of n which denote primes.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(A094535(n)) = n and a(m) < n for m < A094535(n); A039995(39467139) = 100, cf. A205956. - Reinhard Zumkeller, Feb 01 2012
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EXAMPLE
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a(103) = 3; the 3 primes are 3, 13 and 103.
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MATHEMATICA
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cnt[n_] := Module[{d = IntegerDigits[n]}, Length[Union[Select[FromDigits /@ Subsets[d], PrimeQ]]]]; Table[cnt[n], {n, 105}] (* T. D. Noe, Jan 31 2012 *)
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PROG
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(Haskell)
import Data.List (subsequences, nub)
a039995 n = sum $
map a010051 $ nub $ map read (tail $ subsequences $ show n)
-- Reinhard Zumkeller, Jan 31 2012
(Python)
from sympy import isprime
from itertools import chain, combinations as combs
def powerset(s): # nonempty subsets of s
return chain.from_iterable(combs(s, r) for r in range(1, len(s)+1))
def a(n):
ss = set(int("".join(s)) for s in powerset(str(n)))
return sum(1 for k in ss if isprime(k))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Aug 07 2022
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CROSSREFS
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A039997 counts only the primes which occur as substrings, i.e. contiguous subsequences. Cf. A035232.
Cf. A010051.
Sequence in context: A193403 A354272 A039997 * A035232 A359269 A091603
Adjacent sequences: A039992 A039993 A039994 * A039996 A039997 A039998
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KEYWORD
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nonn,base
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AUTHOR
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David W. Wilson
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STATUS
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approved
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