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A182145
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XOR(d1,d2), where d1 and d2 are the difference between consecutive primes given in binary.
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1
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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
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1,1
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COMMENTS
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Conjecture: among values less than 60 the most frequent value is 30 (based on frequencies for n < 2126795281, i.e. primes less than 50176000000).
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, XOR
Wikipedia, Bitwise operation XOR
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FORMULA
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a(n) = (primes(n+2)-primes(n+1)) XOR (primes(n+1)-primes(n)) , where XOR is the bitwise exclusive-OR operator
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EXAMPLE
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(5-3)xor(3-2)=3, (7-5)xor(5-3)=0, (11-7)xor(7-5)=6.
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MATHEMATICA
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nn = 100; d = Differences[Prime[Range[nn+2]]]; Table[BitXor[d[[n]], d[[n+1]]], {n, nn}] (* T. D. Noe, Apr 16 2012 *)
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PROG
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(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
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CROSSREFS
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Cf. A000040, A001223.
Sequence in context: A322579 A004606 A019808 * A201569 A056459 A021330
Adjacent sequences: A182142 A182143 A182144 * A182146 A182147 A182148
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KEYWORD
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nonn,base
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AUTHOR
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Alex Ratushnyak, Apr 14 2012
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STATUS
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approved
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