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

1,1

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.

Links

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

Example

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.

Mathematica

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

Prog

(Scheme, with Antti Karttunen's IntSeq-library) (define A234218 (MATCHING-POS 1 1 (lambda (n) (and (prime? n) (odd? (A000120 (expt n 3))))))) ;; Antti Karttunen, Dec 22 2013
(PARI) is(n)=isprime(n) && hammingweight(n^3)%2 \\ Charles R Greathouse IV, Mar 17 2014

Crossrefs

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

Sequence in context: A018540 A045388 A118796 * A171794 A243615 A243617

Adjacent sequences: A234215 A234216 A234217 * A234219 A234220 A234221

Keyword

nonn,easy

Author

Irina Gerasimova, Dec 21 2013

Extensions

Missing terms added by Antti Karttunen, Dec 22 2013

Status

approved