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A039996
Number of distinct primes embedded in prime(n) as substrings.
73
1, 1, 1, 1, 1, 2, 2, 1, 3, 2, 2, 3, 1, 2, 2, 3, 2, 1, 2, 2, 3, 2, 2, 1, 2, 1, 2, 2, 1, 4, 3, 4, 5, 3, 1, 2, 3, 2, 3, 5, 4, 1, 2, 3, 4, 2, 3, 4, 3, 3, 4, 4, 3, 3, 4, 3, 2, 4, 3, 2, 4, 4, 3, 4, 4, 5, 3, 4, 4, 2, 4, 4, 4, 5, 5, 3, 3, 4, 1, 1, 3, 2, 4, 3, 3, 3, 1, 3, 2, 2, 3, 4, 2, 1, 1, 3, 2, 3, 5, 3, 4, 3, 3, 2, 4
OFFSET
1,6
LINKS
FORMULA
a(n) = A039997(prime(n)).
a(n) <= A039994(n). - Charles R Greathouse IV, Apr 22 2015
EXAMPLE
a(26) = 1 since the only prime substring of "101" is 101.
a(48) = 4 since the only distinct prime substrings of "223" are 2, 3, 23, 223. - David A. Corneth, Jul 06 2020
MATHEMATICA
f[n_] := Block[{id = IntegerDigits@ Prime@n, len = Floor[ Log[10, Prime@n] + 1]}, Count[ PrimeQ@ Union[ FromDigits@# & /@ Flatten[ Table[ Partition[id, k, 1], {k, len}], 1]], True]]; Array[f, 105] (* Robert G. Wilson v, Jun 28 2010 *)
PROG
(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)<n*10, if(isprime(n%t), v=concat(v, n%t))); v=vecsort(v, , 8); n\=10); v
a(n)=#dp(prime(n)) \\ Charles R Greathouse IV, Apr 22 2015
CROSSREFS
Sequence in context: A283004 A111709 A348911 * A039994 A348485 A343188
KEYWORD
nonn,base
EXTENSIONS
Name corrected by David A. Corneth, Jul 06 2020
STATUS
approved