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A205510 Binary Hamming distance between prime(n) and prime(n+1). 20
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
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
Sequence in context: A140086 A037194 A326130 * A330004 A332901 A292583
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 March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)