A094535 -id:A094535 - cp's OEIS frontend

A039995 Number of distinct primes which occur as subsequences of the sequence of digits of n.

0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 2, 0, 1, 0, 2, 0, 1, 1, 1, 1, 3, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 3, 1, 1, 0, 1, 1, 2, 0, 1, 0, 2, 0, 0, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 0, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 2, 2, 3, 1, 2, 1, 1, 1, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 2, 1, 3, 0, 1

Offset: 1

David W. Wilson

a(n) counts subsequences of digits of n which denote primes.

			a(103) = 3; the 3 primes are 3, 13 and 103.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

A039997 counts only the primes which occur as substrings, i.e. contiguous subsequences. Cf. A035232.

Cf. A010051.

import Data.List (subsequences, nub)
a039995 n = sum $
   map a010051 $ nub $ map read (tail $ subsequences $ show n)
-- Reinhard Zumkeller, Jan 31 2012

cnt[n_] := Module[{d = IntegerDigits[n]}, Length[Union[Select[FromDigits /@ Subsets[d], PrimeQ]]]]; Table[cnt[n], {n, 105}] (* T. D. Noe, Jan 31 2012 *)

from sympy import isprime
from itertools import chain, combinations as combs
def powerset(s): # nonempty subsets of s
    return chain.from_iterable(combs(s, r) for r in range(1, len(s)+1))
def a(n):
    ss = set(int("".join(s)) for s in powerset(str(n)))
    return sum(1 for k in ss if isprime(k))
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Aug 07 2022

a(A094535(n)) = n and a(m) < n for m < A094535(n); A039995(39467139) = 100, cf. A205956. - Reinhard Zumkeller, Feb 01 2012

A205956 Distinct primes occurring as not necessarily consecutive subsequences in decimal representation of 39467139.

Original entry on oeis.org

3, 7, 13, 19, 31, 37, 41, 43, 47, 61, 67, 71, 73, 79, 97, 139, 313, 347, 349, 367, 373, 379, 397, 419, 439, 461, 463, 467, 479, 613, 619, 673, 719, 739, 919, 941, 947, 967, 971, 3413, 3461, 3463, 3467, 3469, 3613, 3671, 3673, 3719, 3739, 3919, 3943, 3947

Offset: 1

Reinhard Zumkeller, Feb 02 2012

39467139 is the smallest number containing exactly 100 primes: A094535(100) = 39467139, A039995(39467139) = 100; 39467139 itself is not prime: 39467139 = 3*53*89*2789.

			a(10) = 61        <- ___6_1__;
a(20) = 367       <- 3__67___;
a(30) = 613       <- ___6_13_;
a(40) = 3413      <- 3_4__13_;
a(50) = 3919      <- 39___1_9;
a(60) = 9419      <- _94__1_9;
a(70) = 9719      <- _9__71_9;
a(80) = 39439     <- 394___39;
a(90) = 346139    <- 3_46_139;
a(100) = 3946139  <- 3946_139.

Reinhard Zumkeller, Table of n, a(n) for n = 1..100 (full sequence)

Cf. A010051.

import Data.List (subsequences, nub, sort)
a205956 n = a205956_list !! (n-1)
a205956_list = sort $ filter ((== 1) . a010051) $
                      nub $ map read (tail $ subsequences "39467139")

cp's OEIS Frontend

A039995 Number of distinct primes which occur as subsequences of the sequence of digits of n.

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