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A163496
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a(n) = the number of distinct primes that can be made by writing n in binary, doubling any number (possibly zero) of 1's in place in this binary representation, and converting back to decimal.
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0
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1, 1, 2, 0, 3, 0, 2, 0, 1, 0, 3, 0, 4, 0, 2, 0, 1, 0, 3, 0, 4, 0, 4, 0, 0, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 5, 0, 5, 0, 3, 0, 4, 0, 3, 0, 3, 0, 4, 0, 4, 0, 1, 0, 4, 0, 5, 0, 1, 0, 2, 0, 2, 0, 4, 0, 2, 0, 3, 0, 3, 0, 4, 0, 3, 0, 3, 0, 6, 0, 5, 0, 6, 0, 3, 0, 7, 0, 5, 0, 4, 0, 1, 0, 4, 0, 4, 0, 4, 0, 4
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OFFSET
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1,3
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COMMENTS
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a(2n) = 0, for all n >= 2.
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LINKS
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Table of n, a(n) for n=1..105.
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EXAMPLE
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13 in binary is 1101. The distinct binary numbers that can be made by doubling any number of 1's are: 1101 (13 in decimal), 11011 (doubling the rightmost 1, getting 27 in decimal), 11101 (29), 111101 (61), 111011 (59), and 1111011 (123). Of these, four are primes (13, 29, 61, 59). So a(13) = 4.
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CROSSREFS
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Sequence in context: A212138 A133735 A095704 * A092241 A213266 A182038
Adjacent sequences: A163493 A163494 A163495 * A163497 A163498 A163499
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KEYWORD
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base,nonn
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AUTHOR
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Leroy Quet, Jul 29 2009
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EXTENSIONS
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More terms from Sean A. Irvine, Oct 11 2009
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STATUS
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approved
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