A099653 a(n) is the number of n-subsets (n=1,2,...,10) of the 10 decimal digits from which prime numbers can be constructed including all n distinct digits either with or without repetitions; a(n) <= binomial(10,n).
5, 24, 96, 194, 246, 209, 120, 45, 10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1
Examples
n=1: {11,2,3,5,7} represent the 1-subsets; a(1) = 5;
n=2: A099651 includes least terms of each a(2) = 24 subsets;
n=5: a(5) = binomial(10,5) - binomial(6,5) - binomial(4,5) = 210 - 6 - 0 = 246;
n=6: each of the 6-subsets is good for primes except {0,2,4,5,6,8} so a(6) = 210 - 1.
n=7,8,9,10: a(n) = binomial(10,n).
Total number of relevant subset classes from the 1023 nonempty k-digit subsets equals 950. See also A099654.
Programs
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Mathematica
Table[5 Boole[n == 1] + Binomial[10, n] - Binomial[6, n] - Binomial[4, n], {n, 83}] (* Michael De Vlieger, Jul 24 2017 *)
Formula
a(n) = binomial(10,n) - binomial(6,n) - binomial(4,n); number of n-digit subsets minus "antiprime-digit subclasses" selected from {0, 2, 4, 5, 6, 8} and {0, 3, 6, 9} digit collections.