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%I #35 Nov 15 2022 15:58:44
%S 1,2,1,2,2,3,1,1,2,1,4,2,1,1,3,3,2,6,1,3,2,3,2,3,1,1,2,2,3,3,6,2,1,4,
%T 1,2,5,1,2,4,2,2,6,1,1,2,2,4,2,2,2,4,2,7,2,2,1,3,2,1,5,3,1,3,1,5,3,2,
%U 2,4,2,1,3,3,1,6,1,3,1,4,2,2,4,2,2,5,1,1,1,3,2,3,2,2,1,2,7,1,3,5
%N Binary Hamming distance between prime(n) and prime(n+1).
%C We call "Hamming's twin primes" the pairs of consecutive primes (p,q) with Hamming distance 1. They are (2,3), (5,7), (17,19,), (19,23), (29,31), (41,43), (43,47), (67,71), (97,101), ..., (A205511,A205302). As in Twin Primes Conjecture, we conjecture that there exist infinitely many Hamming's twin pairs.
%H Alois P. Heinz, <a href="/A205510/b205510.txt">Table of n, a(n) for n = 1..20000</a>
%p a:= n-> add(i, i=Bits[GetBits](Bits[Xor](ithprime(n), ithprime(n+1)), 0..-1)):
%p seq(a(n), n=1..100); # _Alois P. Heinz_, Oct 11 2017
%t Table[Count[IntegerDigits[BitXor[Prime[n],Prime[n+1]],2],1],{n,100}] (* _Jayanta Basu_, May 26 2013 *)
%o (PARI) A205510(n)=norml2(binary(bitxor(prime(n),prime(n+1)))) \\ _M. F. Hasler_, Jan 29 2012
%o (PARI) a(n,p=prime(n),q=nextprime(p+1))=hammingweight(bitxor(p,q)) \\ _Charles R Greathouse IV_, Nov 15 2022
%Y Cf. A205511, A205302, A205509, A001511, A345985.
%K nonn,base,easy
%O 1,2
%A _Vladimir Shevelev_, Jan 28 2012
%E Corrected a(24) and a(25) by _M. F. Hasler_, Jan 29 2012
%E Added "binary" to definition. - _N. J. A. Sloane_, Jul 09 2021
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