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 A205510 Binary Hamming distance between prime(n) and prime(n+1). 23
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..20000 MAPLE a:= n-> add(i, i=Bits[GetBits](Bits[Xor](ithprime(n), ithprime(n+1)), 0..-1)): seq(a(n), n=1..100); # Alois P. Heinz, Oct 11 2017 MATHEMATICA Table[Count[IntegerDigits[BitXor[Prime[n], Prime[n+1]], 2], 1], {n, 100}] (* Jayanta Basu, May 26 2013 *) PROG (PARI) A205510(n)=norml2(binary(bitxor(prime(n), prime(n+1)))) \\ M. F. Hasler, Jan 29 2012 (PARI) a(n, p=prime(n), q=nextprime(p+1))=hammingweight(bitxor(p, q)) \\ Charles R Greathouse IV, Nov 15 2022 CROSSREFS Cf. A205511, A205302, A205509, A001511, A345985. Sequence in context: A140086 A037194 A326130 * A330004 A332901 A292583 Adjacent sequences: A205507 A205508 A205509 * A205511 A205512 A205513 KEYWORD nonn,base,easy AUTHOR Vladimir Shevelev, Jan 28 2012 EXTENSIONS Corrected a(24) and a(25) by M. F. Hasler, Jan 29 2012 Added "binary" to definition. - N. J. A. Sloane, Jul 09 2021 STATUS approved

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Last modified September 9 22:43 EDT 2024. Contains 375765 sequences. (Running on oeis4.)