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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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12
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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
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internal format)
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OFFSET
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1,13
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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(A062115(n)) = 0; a(A093301(n)) = n and a(m) <> n for m < A093301(n). - Reinhard Zumkeller, Jul 16 2007
a(A163753(n)) > 0; a(A205667(n)) = 1. [Reinhard Zumkeller, Jan 31 2012]
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EXAMPLE
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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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MAPLE
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a:= n-> (s-> nops(select(t -> t[1]<>"0" and isprime(parse(t)),
{seq(seq(s[i..j], i=1..j), j=1..length(s))})))(""||n):
seq(a(n), n=1..100); # Alois P. Heinz, Aug 09 2022
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MATHEMATICA
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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
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(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
(PARI) dp(n)=if(n<12, return(if(isprime(n), [n], []))); my(v=vecsort(select(isprime, eval(Vec(Str(n)))), , 8), t); while(n>9, if(gcd(n%10, 10)>1, n\=10; next); t=10; while((t*=10)<n*10, if(isprime(n%t), v=concat(v, n%t))); v=vecsort(v, , 8); n\=10); v
a(n)=#dp(n) \\ Charles R Greathouse IV, Jul 10 2012
(Python)
from sympy import isprime
def a(n):
s = str(n)
ss = (int(s[i:j]) for i in range(len(s)) for j in range(i+1, len(s)+1))
return len(set(k 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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Different from A039995 after the 100th term. Cf. A035232.
Sequence in context: A113686 A193403 A354272 * A039995 A035232 A359269
Adjacent sequences: A039994 A039995 A039996 * A039998 A039999 A040000
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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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EXTENSIONS
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Edited by Robert G. Wilson v, Feb 24 2003
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STATUS
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approved
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