A234218 Primes whose cubes are odious.

2, 13, 23, 29, 43, 59, 61, 67, 71, 73, 79, 89, 97, 101, 103, 109, 113, 131, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 229, 241, 251, 293, 311, 313, 337, 353, 367, 383, 389, 397, 409, 419, 431, 439, 443, 461, 467, 479, 499, 509, 521, 541, 563, 577, 601

Offset: 1

Author

Irina Gerasimova, Dec 21 2013

Keywords

• nonn
• easy

Comments

Primes p with odious p^3.

Note: "odious" means having an odd number of 1-bits in number's binary representation. So, put in another way, primes p such that A010060(A000578(p)) = 1. - Antti Karttunen, Dec 22 2013

Subsequence of the numbers 1, 2, 4, 8, 13, 16, 23, 25, 26, 29, 32, 35, 43, 45, 46, ... which have odious cubes.

Examples

			Prime 2 is in this sequence because 2^3 = 8 and 8 is odious number. Prime 13 is in this sequence because 13*3 = 2197 and 2197 is odious number.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1001

Crossrefs

Cf. A000069, A000120, A000578, A010060, A125498, A192085, A194991.

Programs

Mathematica

Select[Prime[Range[1000]], OddQ[DigitCount[#^3, 2, 1]] &] (* Indranil Ghosh, Apr 02 2017 *)

PARI

is(n)=isprime(n) && hammingweight(n^3)%2 \\ Charles R Greathouse IV, Mar 17 2014

Extensions

Missing terms added by Antti Karttunen, Dec 22 2013