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Search: id:A099653
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| A099653 |
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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]<=C[10,n]. |
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+0
5
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| 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a[n]=C[10, n]-C[6, n]-C[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.
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EXAMPLE
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n=1: {11,2,3,5,7} represent the 1-subsets; a[1]=5
n=2: A099651 incudes least terms of each a[2]=24 subsets;
n=5: a[5]=C[10,5]-C[6,5]-C[4,5]=210-6-0=246;
n=6: each 6-subsets are good for primes except {0,2,4,5,6,8} so a[6]=210-1.
n=7,8,9,10: a[n]=C[10,n].
Total number of relevant subset-classes from the 1023 non-empty k-digit-subsets equals 950. See also A099654.
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CROSSREFS
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Cf. A099651, A099654, A099756.
Sequence in context: A145914 A066316 A087095 this_sequence A078820 A046724 A008464
Adjacent sequences: A099650 A099651 A099652 this_sequence A099654 A099655 A099656
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KEYWORD
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base,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 15 2004
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