

A236514


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


2



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
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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



