A071600 Numbers k such that k and prime(k) have the same number of 1's in their binary representation.

1, 3, 13, 19, 21, 23, 25, 30, 44, 45, 47, 57, 60, 61, 71, 77, 98, 99, 101, 103, 107, 108, 110, 118, 121, 125, 158, 159, 178, 179, 184, 186, 187, 188, 209, 215, 218, 221, 237, 244, 246, 247, 248, 249, 251, 279, 287, 312, 334, 335, 346, 350, 359, 361, 362, 365

Offset: 1

Author

Benoit Cloitre, Jun 01 2002

Keywords

• base
• easy
• nonn

Examples

			221 = 11011101 in base 2, prime(221) = 1381 = 10101100101 in base 2, both have 6 "1's" in their binary representation, hence 221 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Crossrefs

Cf. A000120, A014499, A033549, A049084, A072439, A090455.

Programs

Mathematica

Select[Range[400],DigitCount[#,2,1]==DigitCount[Prime[#],2,1]&] (* Harvey P. Dale, Mar 09 2015 *)

PARI

for(n=1,1000,s=1; if(sum(i=1,length(binary(n)), component(binary(n),i))==sum(i=1,length(binary(prime(n))), component(binary(prime(n)),i)),print1(n,",")))

PARI

is(n)=hammingweight(n)==hammingweight(prime(n)) \\ Charles R Greathouse IV, Mar 07 2013

Formula

a(n) = A049084(A072439(n)); A000120(a(n)) = A000120(A072439(n)). - Reinhard Zumkeller, Jun 17 2002

A090455(a(n)) = 0, A000120(a(n)) = A014499(a(n)).