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

1,1

Comments

Number of "antiprime-digit-subclasses".

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

Links

Table of n, a(n) for n=1..131.

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Cf. A099651, A099654, A099756.

Sequence in context: A004163 A350328 A113410 * A195959 A228141 A268527

Adjacent sequences: A099651 A099652 A099653 * A099655 A099656 A099657

Keyword

base,nonn

Author

Labos Elemer, Nov 15 2004

Status

approved