A194991 -id:A194991 - cp's OEIS frontend

A235331 Numbers with odious squares.

1, 2, 4, 5, 7, 8, 9, 10, 11, 14, 16, 17, 18, 19, 20, 22, 23, 25, 28, 29, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 46, 49, 50, 51, 55, 56, 58, 59, 62, 64, 65, 66, 67, 68, 70, 71, 72, 75, 76, 77, 78, 79, 80, 82, 85, 86, 87, 88, 89, 91, 92, 95, 97, 98, 100

Offset: 1

Gerasimov Sergey, Jan 06 2014

Numbers that are sqrt(odious squares).

			1 = sqrt(A235001(1)) = sqrt(1).
2 = sqrt(A235001(2)) = sqrt(4).
4 = sqrt(A235001(3)) = sqrt(16).
5 = sqrt(A235001(4)) = sqrt(25).

Vincenzo Librandi, Table of n, a(n) for n = 1..2600

Cf. A235001, A194991.

[n : n in [0..130] |IsOdd(&+Intseq(n^2, 2))]; // Vincenzo Librandi, Jan 31 2018

Select[Range[200], OddQ[DigitCount[#^2, 2][[1]]] &] (* Vincenzo Librandi, Jan 31 2018 *)

isok(n) = (hammingweight(n^2) % 2) == 1; \\ Michel Marcus, Jan 31 2018

a(n) = sqrt(A235001(n)).

A234218 Primes whose cubes are odious.

Original entry on oeis.org

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

Irina Gerasimova, Dec 21 2013

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.

			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.

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

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

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

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

Missing terms added by Antti Karttunen, Dec 22 2013

cp's OEIS Frontend

A235331 Numbers with odious squares.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula