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

1,2

Links

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

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)).

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A024685 A024474 A024599 * A260802 A338341 A045435

Adjacent sequences: A071597 A071598 A071599 * A071601 A071602 A071603

Keyword

base,easy,nonn

Author

Benoit Cloitre, Jun 01 2002

Status

approved