This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A205510 #35 Nov 15 2022 15:58:44
%S A205510 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 A205510 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 A205510 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 A205510 Binary Hamming distance between prime(n) and prime(n+1).
%C A205510 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 A205510 Alois P. Heinz, <a href="/A205510/b205510.txt">Table of n, a(n) for n = 1..20000</a>
%p A205510 a:= n-> add(i, i=Bits[GetBits](Bits[Xor](ithprime(n), ithprime(n+1)), 0..-1)):
%p A205510 seq(a(n), n=1..100); # _Alois P. Heinz_, Oct 11 2017
%t A205510 Table[Count[IntegerDigits[BitXor[Prime[n],Prime[n+1]],2],1],{n,100}] (* _Jayanta Basu_, May 26 2013 *)
%o A205510 (PARI) A205510(n)=norml2(binary(bitxor(prime(n),prime(n+1)))) \\ _M. F. Hasler_, Jan 29 2012
%o A205510 (PARI) a(n,p=prime(n),q=nextprime(p+1))=hammingweight(bitxor(p,q)) \\ _Charles R Greathouse IV_, Nov 15 2022
%Y A205510 Cf. A205511, A205302, A205509, A001511, A345985.
%K A205510 nonn,base,easy
%O A205510 1,2
%A A205510 _Vladimir Shevelev_, Jan 28 2012
%E A205510 Corrected a(24) and a(25) by _M. F. Hasler_, Jan 29 2012
%E A205510 Added "binary" to definition. - _N. J. A. Sloane_, Jul 09 2021