A163496 - OEIS

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, 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

Index entries for sequences related to binary expansion of n

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

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