A099654 a(n) is the number of n-subsets [n=1,2,...,10] of the 10 decimal digits from which no prime numbers can be constructed. See also A099653.

5, 21, 24, 16, 6, 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, 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

Author

Labos Elemer, Nov 15 2004

Keywords

• base
• nonn

Comments

Number of "antiprime-digit-subclasses".

Subsets were selected from {0, 2, 4, 5, 6, 8} and {0, 3, 6, 9} digit collections.

Examples

			n=1: {0,2,4,6,8} represent the relevant 1-subsets so a[1]=5.
Total number of prime irrelevant subset-classes from the 1023 nonempty k-digit-subsets equals 5 + 21 + 24 + 16 + 6 + 1 = 73 = 1023 - 950. See also A099653.
The "antiprime n-digit-collections" are taken from {0,2,4,5,6,8} or {0,3,6,9}, of which only composites can be constructed.
		

Crossrefs

Cf. A099651, A099654, A099756.

Programs

Mathematica

Table[Binomial[6, n] + Binomial[4, n] - 5 Boole[n == 1], {n, 100}] (* Michael De Vlieger, Mar 26 2017 *)

PARI

a(n) = binomial(6, n) + binomial(4, n) - 5*(n==1); \\ Indranil Ghosh, Mar 27 2017

Python

from sympy import binomial
def a(n): return binomial(6, n) + binomial(4, n) - 5*(n==1) # Indranil Ghosh, Mar 27 2017

Formula

a(n) = binomial(6,n) + binomial(4,n) for n > 1.