cp's OEIS Frontend

A035232 Number of substrings of n which are primes (counted with multiplicity).

%I A035232 #16 Nov 15 2022 11:42:29
%S A035232 0,1,1,0,1,0,1,0,0,0,1,1,2,0,1,0,2,0,1,1,1,2,3,1,2,1,2,1,2,1,2,2,2,1,
%T A035232 2,1,3,1,1,0,1,1,2,0,1,0,2,0,0,1,1,2,3,1,2,1,2,1,2,0,1,1,1,0,1,0,2,0,
%U A035232 0,1,2,2,3,1,2,1,2,1,2,0,0,1,2,0,1,0,1,0,1,0,0,1,1,0,1,0,2,0,0,0,1,1,2,0,1
%N A035232 Number of substrings of n which are primes (counted with multiplicity).
%C A035232 No leading 0's allowed in substrings.
%H A035232 Michael S. Branicky, <a href="/A035232/b035232.txt">Table of n, a(n) for n = 1..10000</a>
%F A035232 Trivial upper bound: a(n) <= binomial(floor(log(n)/log(10)+2), 2) ~ k*log^2 n with k = 0.09430584850580... = 1/log(10)^2/2. - _Charles R Greathouse IV_, Nov 15 2022
%e A035232 The primes occurring as substrings of 37 are 3, 7, 37, so a(37) = 3.
%e A035232 a(22) = 2, since the prime 2 occurs twice as a substring.
%p A035232 a:= n-> (s-> nops(select(t -> t[1]<>"0" and isprime(parse(t)),
%p A035232         [seq(seq(s[i..j], i=1..j), j=1..length(s))])))(""||n):
%p A035232 seq(a(n), n=1..100);  # _Alois P. Heinz_, Aug 07 2022
%t A035232 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[d], True]]; Table[ a[n], {n, 1, 105}]
%o A035232 (Python)
%o A035232 from sympy import isprime
%o A035232 def a(n):
%o A035232     s = str(n)
%o A035232     ss = (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1))
%o A035232     return sum(1 for w in ss if w[0] != "0" and isprime(int(w)))
%o A035232 print([a(n) for n in range(1, 106)]) # _Michael S. Branicky_, Aug 07 2022
%Y A035232 Cf. A039997, A039995.
%K A035232 base,easy,nonn
%O A035232 1,13
%A A035232 _Erich Friedman_
%E A035232 Edited by _Robert G. Wilson v_, Feb 24 2003