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A035232 Number of substrings of n which are primes (counted with multiplicity). 62
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,13
COMMENTS
No leading 0's allowed in substrings.
LINKS
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
Sequence in context: A354272 A039997 A039995 * A359269 A091603 A370884
KEYWORD
base,easy,nonn
AUTHOR
EXTENSIONS
Edited by Robert G. Wilson v, Feb 24 2003
STATUS
approved

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Last modified April 25 09:49 EDT 2024. Contains 371967 sequences. (Running on oeis4.)