

A182145


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


1



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
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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 exclusiveOR operator


EXAMPLE

(53)xor(32)=3, (75)xor(53)=0, (117)xor(75)=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 !! (n1)
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 A056459 A021330
Adjacent sequences: A182142 A182143 A182144 * A182146 A182147 A182148


KEYWORD

nonn,base


AUTHOR

Alex Ratushnyak, Apr 14 2012


STATUS

approved



