A235331 -id:A235331 - cp's OEIS frontend

A194991 Primes whose squares are odious.

2, 5, 7, 11, 17, 19, 23, 29, 31, 41, 43, 59, 67, 71, 79, 89, 97, 101, 103, 113, 127, 131, 139, 149, 157, 163, 167, 173, 179, 181, 193, 197, 223, 227, 229, 239, 251, 257, 263, 271, 283, 307, 313, 349, 353, 373, 379, 383, 389, 401, 409, 421, 431, 433, 439, 449, 457, 467, 479, 487, 509, 523, 547, 563

Offset: 1

Vladimir Shevelev, Sep 07 2011

Subsequence of the numbers 1, 2, 4, 5, 7, 8, 9, 10, 11, 14, 16, 17, 18, 19, 20, 22, 23, 25, 28, 29, 31, 32, 33, ... which have odious squares. See A235331. - R. J. Mathar, Sep 20 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..5240

Cf. A000069, A001969, A027697, A027699.

[p : p in PrimesInInterval(2, 600) |IsOdd(&+Intseq(p^2, 2))]; // Vincenzo Librandi, Dec 15 2018

Select[Prime@ Range@ 120, OddQ@ First@ DigitCount[#^2, 2] &] (* Amiram Eldar, Dec 14 2018 after Michael De Vlieger at A027697 *)

isok(p) = isprime(p) && (hammingweight(p^2) % 2); \\ Michel Marcus, Dec 14 2018

A298879 Numbers whose square is not odious.

Original entry on oeis.org

0, 3, 6, 12, 13, 15, 21, 24, 26, 27, 30, 37, 42, 45, 47, 48, 52, 53, 54, 57, 60, 61, 63, 69, 73, 74, 81, 83, 84, 90, 93, 94, 96, 99, 104, 105, 106, 107, 108, 109, 111, 114, 115, 119, 120, 122, 123, 126, 133, 137, 138, 141, 146, 148, 151, 155, 159

Offset: 1

Vincenzo Librandi, Jan 31 2018

Complement of A235331.
From Robert Israel, Feb 02 2018: (Start)
2*n is in the sequence if and only if n is in the sequence.
2*n+1 is in the sequence if and only if n*(n+1) is odious. (End)

Cf. A235001, A235331.

[n: n in [0..200] | IsEven(&+Intseq(n^2, 2))];

select(t -> convert(convert(t^2,base,2),`+`)::even, [$0..200]); # Robert Israel, Feb 02 2018

Join[{0}, Select[Range[200], !OddQ[DigitCount[#^2, 2][[1]]] &]]

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

cp's OEIS Frontend

A194991 Primes whose squares are odious.

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