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A099654
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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.
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5
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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
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OFFSET
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1,1
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COMMENTS
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Number of "antiprime-digit-subclasses".
Subsets were selected from {0, 2, 4, 5, 6, 8} and {0, 3, 6, 9} digit collections.
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LINKS
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FORMULA
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a(n) = binomial(6,n) + binomial(4,n) for n > 1.
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EXAMPLE
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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.
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MATHEMATICA
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Table[Binomial[6, n] + Binomial[4, n] - 5 Boole[n == 1], {n, 100}] (* Michael De Vlieger, Mar 26 2017 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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