login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A205510 Hamming distance between prime(n) and prime(n+1). 19
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),... 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

CROSSREFS

Cf. A001511, A205509.

Sequence in context: A140086 A037194 A326130 * A292583 A111630 A305301

Adjacent sequences:  A205507 A205508 A205509 * A205511 A205512 A205513

KEYWORD

nonn,base

AUTHOR

Vladimir Shevelev, Jan 28 2012

EXTENSIONS

Corrected a(24) and a(25) by M. F. Hasler, Jan 29 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 19 23:39 EDT 2019. Contains 324222 sequences. (Running on oeis4.)