A363790 Numbers k such that k and k+1 are both primitive binary Niven numbers (A363787).

115, 155, 204, 284, 355, 395, 404, 555, 564, 595, 675, 804, 835, 846, 1075, 1124, 1164, 1182, 1266, 1315, 1434, 1555, 1604, 1686, 1795, 1938, 2075, 2124, 2195, 2244, 2315, 2324, 2358, 2435, 2595, 3084, 3204, 3282, 3366, 4124, 4195, 4206, 4235, 4244, 4364, 4458

Offset: 1

Author

Amiram Eldar, Jun 22 2023

Keywords

• nonn
• base

Examples

			115 is a term since 115 and 116 are both primitive binary Niven numbers.
		

Links

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

Crossrefs

Subsequence of A049445, A330931 and A363787.

Subsequences: A363791, A363792.

Programs

Mathematica

binNivQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; q[n_] := binNivQ[n] && ! (EvenQ[n] && binNivQ[n/2]); Select[Range[5000], q[#] && q[# + 1] &]

PARI

isbinniv(n) = !(n % hammingweight(n));
isprim(n) = isbinniv(n) && !(!(n%2) && isbinniv(n/2));
is(n) = isprim(n) && isprim(n+1);