# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a099654 Showing 1-1 of 1 %I A099654 #14 Mar 28 2017 15:05:48 %S A099654 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, %T A099654 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, %U A099654 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 %N 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. %C A099654 Number of "antiprime-digit-subclasses". %C A099654 Subsets were selected from {0, 2, 4, 5, 6, 8} and {0, 3, 6, 9} digit collections. %F A099654 a(n) = binomial(6,n) + binomial(4,n) for n > 1. %e A099654 n=1: {0,2,4,6,8} represent the relevant 1-subsets so a[1]=5. %e A099654 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. %e A099654 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. %t A099654 Table[Binomial[6, n] + Binomial[4, n] - 5 Boole[n == 1], {n, 100}] (* _Michael De Vlieger_, Mar 26 2017 *) %o A099654 (PARI) a(n) = binomial(6, n) + binomial(4, n) - 5*(n==1); \\ _Indranil Ghosh_, Mar 27 2017 %o A099654 (Python) %o A099654 from sympy import binomial %o A099654 def a(n): return binomial(6, n) + binomial(4, n) - 5*(n==1) # _Indranil Ghosh_, Mar 27 2017 %Y A099654 Cf. A099651, A099654, A099756. %K A099654 base,nonn %O A099654 1,1 %A A099654 _Labos Elemer_, Nov 15 2004 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE