This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A337077 #10 Aug 17 2020 22:48:01
%S A337077 1,2,12,24,96,690,1386,3024,3738,3794,5544,22834,57278,68908,89060,
%T A337077 196240,360000,388421,524160,1556360,1572480,2359140,3929940,8057711,
%U A337077 11484900,15201585,16115505,19910436,32444160,7348411575,16097143458,33273395232,51333952011
%N A337077 Binary Niven numbers (A049445) with a record gap to the next binary Niven number.
%C A337077 The corresponding record gaps are 1, 2, 4, 8, 12, 18, 26, 27, 33, 38, 42, 44, 46, 50, 58, 68, 74, 77, 103, 109, 122, 137, 156, 157, 165, 189, 191, 204, 240, 265, 267, 312, 333, ...
%C A337077 De Koninck, Doyon and Kátai (2003) proved that the asymptotic density of the Niven numbers in any base >= 2 is 0. Therefore, the asymptotic density of the binary Niven numbers is 0 and this sequence is infinite.
%H A337077 Jean-Marie De Koninck and Nicolas Doyon, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Doyon/doyon.html">Large and Small Gaps Between Consecutive Niven Numbers</a>, J. Integer Seqs., Vol. 6, 2003, Article 03.2.5.
%H A337077 Jean-Marie De Koninck, Nicolas Doyon and Imre Kátai, <a href="https://eudml.org/doc/278575">On the counting function for the Niven numbers</a>, Acta Arithmetica, Vol. 106, No. 3 (2003), 265-275.
%e A337077 The first 8 binary Niven numbers are 1, 2, 4, 6, 8, 10, 12 and 16. The differences between them are 1, 2, 2, 2, 2, 2 and 4. The record gaps, 1, 2 and 4, occur at 1, 2 and 12.
%t A337077 binNivenQ[n_] := Divisible[n, DigitCount[n, 2, 1]]; gapmax = 0; n1 = 1; s = {}; Do[If[binNivenQ[n], gap = n - n1; If[gap > gapmax, gapmax = gap; AppendTo[s, n1]]; n1 = n], {n, 2, 10^6}]; s
%Y A337077 Cf. A049445, A330931, A337076.
%K A337077 nonn,base
%O A337077 1,2
%A A337077 _Amiram Eldar_, Aug 14 2020