A182145 XOR(d1,d2), where d1 and d2 are the difference between consecutive primes given in binary.

3, 0, 6, 6, 6, 6, 6, 2, 4, 4, 2, 6, 6, 2, 0, 4, 4, 2, 6, 4, 2, 2, 14, 12, 6, 6, 6, 6, 10, 10, 2, 4, 8, 8, 4, 0, 2, 2, 0, 4, 8, 8, 6, 6, 14, 0, 8, 6, 6, 2, 4, 8, 12, 0, 0, 4, 4, 2, 6, 8, 4, 10, 6, 6, 10, 8, 12, 8, 6, 2, 14, 14, 0, 2, 2, 14, 12, 12, 2, 8, 8, 8

Offset

1,1

Comments

Conjecture: among values less than 60 the most frequent value is 30 (based on frequencies for n < 2126795281, i.e. primes less than 50176000000).

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, XOR

Wikipedia, Bitwise operation XOR

Formula

a(n) = (primes(n+2)-primes(n+1)) XOR (primes(n+1)-primes(n)), where XOR is the bitwise exclusive-OR operator

Example

(5-3)xor(3-2)=3, (7-5)xor(5-3)=0, (11-7)xor(7-5)=6.

Mathematica

nn = 100; d = Differences[Prime[Range[nn+2]]]; Table[BitXor[d[[n]], d[[n+1]]], {n, nn}] (* T. D. Noe, Apr 16 2012 *)

Prog

(Haskell)
import Data.Bits (xor)
a182145 n = a182145_list !! (n-1)
a182145_list = zipWith xor a001223_list $ tail a001223_list :: [Integer]
-- Reinhard Zumkeller, Apr 23 2012

Crossrefs

Cf. A000040, A001223.

Sequence in context: A322579 A004606 A019808 * A201569 A392252 A056459

Adjacent sequences: A182142 A182143 A182144 * A182146 A182147 A182148

Keyword

nonn,base

Author

Alex Ratushnyak, Apr 14 2012

Status

approved