A039997 Number of distinct primes which occur as substrings of the digits of n.
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
Offset: 1
Examples
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.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Programs
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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 -
Maple
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 -
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}] -
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)
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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
Formula
a(A062115(n)) = 0; a(A093301(n)) = n and a(m) <> n for m < A093301(n). - Reinhard Zumkeller, Jul 16 2007
Extensions
Edited by Robert G. Wilson v, Feb 24 2003
Comments