OFFSET
1,13
COMMENTS
No leading 0's allowed in substrings.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..10000
FORMULA
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
EXAMPLE
The primes occurring as substrings of 37 are 3, 7, 37, so a(37) = 3.
a(22) = 2, since the prime 2 occurs twice as a substring.
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 07 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[d], True]]; Table[ a[n], {n, 1, 105}]
PROG
(Python)
from sympy import isprime
def a(n):
s = str(n)
ss = (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1))
return sum(1 for w in ss if w[0] != "0" and isprime(int(w)))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Aug 07 2022
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
EXTENSIONS
Edited by Robert G. Wilson v, Feb 24 2003
STATUS
approved