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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 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 Cf. A039997, A039995. Sequence in context: A354272 A039997 A039995 * A359269 A091603 A370884 Adjacent sequences: A035229 A035230 A035231 * A035233 A035234 A035235 KEYWORD base,easy,nonn AUTHOR Erich Friedman 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.)