A231271 Numbers k such that k and k+d are both odious (A000069) or both evil (A001969) for every divisor d of k.

1, 5, 7, 9, 13, 17, 23, 29, 31, 37, 41, 49, 53, 61, 71, 73, 85, 89, 97, 101, 103, 109, 113, 119, 125, 127, 129, 133, 137, 149, 151, 157, 167, 173, 181, 193, 197, 199, 217, 223, 229, 233, 241, 249, 257, 263, 269, 277, 281, 293, 311, 313, 317, 321, 325, 337, 341

Offset

1,2

Comments

A prime p is a term iff its binary expansion ends in odd number of 1's (A095283). All terms are in A079523.

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..10000

Example

The odious number k = 341 has divisors {1, 11, 31, 341}. Since the numbers 341 + 1 = 342, 341 + 11 = 352, 341 + 31 = 372, 341 + 341 = 682 are all odious, then 341 is a term.

Mathematica

odiousQ[n_] := OddQ[DigitCount[n, 2][[1]]]; selQ[n_] := Length[Union[Map[odiousQ, Flatten[{n, Map[n+#&, Divisors[n]]}]]]] == 1; Select[Range[200], selQ] (* Peter J. C. Moses, Nov 08 2013 *)

Prog

(PARI) is(k) = {my(hw = hammingweight(k) % 2); fordiv(k, d, if(hammingweight(k+d) % 2 != hw, return(0))); 1; } \\ Amiram Eldar, Aug 12 2024

Crossrefs

Cf. A000069, A001969, A079523, A095283.

Sequence in context: A111083 A050550 A079523 * A359198 A039504 A097280

Adjacent sequences: A231268 A231269 A231270 * A231272 A231273 A231274

Keyword

nonn,base

Author

Vladimir Shevelev, Nov 06 2013

Extensions

More terms from Peter J. C. Moses, Nov 08 2013

Status

approved