A358255 -id:A358255 - cp's OEIS frontend

A363788 Even primitive binary Niven numbers: even terms of A363787.

6, 10, 18, 34, 60, 66, 92, 108, 116, 126, 130, 156, 172, 180, 204, 212, 222, 228, 246, 258, 284, 300, 308, 318, 332, 340, 356, 366, 378, 396, 404, 414, 420, 438, 452, 462, 474, 486, 498, 514, 540, 556, 564, 588, 596, 606, 612, 630, 652, 660, 676, 708, 726, 780

Offset: 1

Amiram Eldar, Jun 22 2023

The odd terms of A363787 are all the odd binary Niven numbers (A144302).

This sequence is infinite. E.g., A052548(k) = 2^k + 2 is a term for all k >= 2.

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

Subsequence of A049445 and A363787.
Equals A363787 \ A144302.
Cf. A052548, A358255 (decimal analog).

binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; q[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]); Select[Range[2, 1000, 2], q]

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

A358256 a(n) is the smallest primitive Niven number ending with n zeros.

Original entry on oeis.org

1, 110, 1300, 17000, 790000, 59900000, 19999999000000, 2999999999999990000000, 4999999999999999999999999999900000000, 899999999999999999999999999999999999999999999999999999999000000000

Offset: 0

Bernard Schott, Nov 05 2022

1 is a primitive Niven number, not ending with 0, so a(0)=1.

a(n) is the smallest term of A358255 that ends with n zeros for n > 0.

			1300 is divisible by 1+3=4, but 13 and 130 are not divisible by 4; 1300 is the smallest such integer ending with two 0's, so a(2) = 1300.

Giovanni Resta, Harshad numbers.

Cf. A005349, A051885, A358255.

a(n) = A051885(2^n)*10^n for n > 3. - Rémy Sigrist, Nov 05 2022

cp's OEIS Frontend

A363788 Even primitive binary Niven numbers: even terms of A363787.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI