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A163496
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.
1
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
OFFSET
1,3
COMMENTS
a(2n) = 0, for all n >= 2.
EXAMPLE
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.
PROG
(PARI) A163496(n, x=0, w=0, z=1) = if(1==n, isprime(x+2^w)+z*isprime(x+3*(2^w)), if(!(n%2), A163496(n/2, x, w+1, 1), A163496(n\2, x+(2^w), w+1, 0)+if(z, A163496(n\2, x+3*(2^w), w+2, z), 0))); \\ Antti Karttunen, Jan 30 2020
CROSSREFS
Sequence in context: A238801 A095704 A351964 * A375519 A092241 A336124
KEYWORD
base,nonn,look
AUTHOR
Leroy Quet, Jul 29 2009
EXTENSIONS
More terms from Sean A. Irvine, Oct 11 2009
STATUS
approved