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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(2n) = 0, for all n >= 2. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 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: A133735 A238801 A095704 * A092241 A336124 A256580 Adjacent sequences:  A163493 A163494 A163495 * A163497 A163498 A163499 KEYWORD base,nonn,look AUTHOR Leroy Quet, Jul 29 2009 EXTENSIONS More terms from Sean A. Irvine, Oct 11 2009 STATUS approved

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)