A236514 Primes with a binary weight greater than or equal to the binary weight of their squares.

2, 3, 7, 23, 31, 47, 79, 127, 157, 191, 223, 317, 367, 379, 383, 479, 727, 751, 887, 1087, 1151, 1277, 1279, 1451, 1471, 1531, 1663, 1783, 1789, 1951, 2297, 2557, 2927, 3067, 3259, 3319, 3581, 3583, 3967, 4253, 4349, 5119, 5231, 5503, 5807, 5821, 6079, 6143, 6271, 6653, 6871, 6911, 7039, 7103, 7151

Offset

1,1

Comments

Primes p such that A000120(p) = A000120(p^2): 2, 3, 7, 31, 79, 127, 157, 317, 379, 751, 1087, 1151, 1277, 1279,...

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

Primes p such that A000120(p) >= A000120(p^2).

Example

2 is in this sequence because 2 is 10 in binary representation, and it has as many 1s as its square 4, which is 100 in binary.

Mathematica

bc[n_] := DigitCount[n, 2][[1]]; Select[Range[7151], PrimeQ[#] && bc[#] >= bc[#^2] &] (* Giovanni Resta, Jan 28 2014 *)
Select[Prime[Range[1000]], DigitCount[#, 2, 1] >= DigitCount[#^2, 2, 1] &] (* Alonso del Arte, Jan 28 2014 *)

Prog

(PARI) is(n)=hammingweight(n^2)<=hammingweight(n) && isprime(n) \\ Charles R Greathouse IV, Mar 18 2014

Crossrefs

Cf. A077436, A094694.

Sequence in context: A093363 A291525 A248346 * A211997 A127581 A278477

Adjacent sequences: A236511 A236512 A236513 * A236515 A236516 A236517

Keyword

nonn,base

Author

Irina Gerasimova, Jan 27 2014

Status

approved