A076775 Greatest common divisor of n and the binary representation of n interpreted decimally.

1, 2, 1, 4, 1, 2, 1, 8, 1, 10, 1, 4, 1, 2, 1, 16, 1, 2, 1, 20, 21, 2, 1, 8, 1, 2, 1, 4, 1, 10, 1, 32, 11, 2, 1, 4, 1, 2, 1, 40, 1, 42, 1, 4, 1, 2, 1, 16, 1, 10, 1, 4, 1, 2, 1, 8, 1, 2, 1, 20, 1, 2, 21, 64, 1, 22, 1, 4, 3, 10, 1, 8, 1, 2, 1, 4, 1, 2, 1, 80, 3, 2, 1, 84, 1, 2, 1, 8, 1, 10, 1

Offset: 1

Author

Reinhard Zumkeller, Nov 14 2002

Keywords

• nonn
• base

Examples

			12 is '1100' in binary representation: a(12) = gcd(12,1100) = gcd(3*2^2,11*5^2*2^2) = 4.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A007088.

Programs

Mathematica

Table[GCD[n,FromDigits[IntegerDigits[n,2]]],{n,100}] (* Harvey P. Dale, Jun 18 2014 *)

PARI

A007088(n) = fromdigits(binary(n), 10); \\ From A007088.
A076775(n) = gcd(n, A007088(n)); \\ Antti Karttunen, May 18 2019

Python

from math import gcd
def A076775(n): return gcd(n,int(bin(n)[2:])) # Chai Wah Wu, Sep 12 2022