A363787 Primitive binary Niven numbers: binary Niven numbers (A049445) that are not twice another binary Niven number.

1, 6, 10, 18, 21, 34, 55, 60, 66, 69, 81, 92, 108, 115, 116, 126, 130, 155, 156, 172, 180, 185, 204, 205, 212, 222, 228, 246, 258, 261, 273, 284, 285, 295, 300, 308, 318, 321, 332, 340, 345, 355, 356, 366, 378, 395, 396, 404, 405, 414, 420, 425, 438, 452, 462

Offset

1,2

Comments

Every binary Niven number is of the form m*2^k, where m is a term of this sequence and k >= 0.

Includes all the odd binary Niven numbers (A144302).

This sequence is infinite. E.g., 16^k + 4^k + 1 is a term for all k >= 1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

6 is a term as 6 is a binary Niven number and 6/2 = 3 is not a binary Niven number.

Mathematica

binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; q[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]); Select[Range[500], q]

Prog

(PARI) isbinniv(n) = !(n % hammingweight(n));
is(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));

Crossrefs

Subsequence of A049445.

Disjoint union of A144302 and A363788.

A363789 is a subsequence.

Cf. A356349 (decimal analog).

Sequence in context: A344882 A344975 A315360 * A315361 A315362 A376927

Adjacent sequences: A363784 A363785 A363786 * A363788 A363789 A363790

Keyword

nonn,easy,base

Author

Amiram Eldar, Jun 22 2023

Status

approved