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 A330933 #22 Jan 05 2025 19:51:41
%S A330933 6222,33102,53262,66702,94830,221550,268302,284910,295182,300750,
%T A330933 316590,364110,379950,427470,533950,554190,570030,590862,617550,
%U A330933 633390,696750,791790,807630,855150,870990,902670,934350,1081422,1140270,1282830,1314510,1330350,1343502
%N A330933 Starts of runs of 4 consecutive Niven numbers in base 2 (A049445).
%C A330933 Cai proved that there are infinitely many runs of 4 consecutive Niven numbers in base 2.
%C A330933 Grundman proved that there are no runs of 5 or more consecutive Niven numbers in base 2.
%D A330933 József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 382.
%H A330933 Amiram Eldar, <a href="/A330933/b330933.txt">Table of n, a(n) for n = 1..10000</a>
%H A330933 Tianxin Cai, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/34-2/cai1.pdf">On 2-Niven numbers and 3-Niven numbers</a>, Fibonacci Quarterly, Vol. 34, No. 2 (1996), pp. 118-120.
%H A330933 Helen G. Grundman, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/32-2/grundman.pdf">Sequences of consecutive Niven numbers</a>, Fibonacci Quarterly, Vol. 32, No. 2 (1994), pp. 174-175.
%H A330933 Wikipedia, <a href="https://en.wikipedia.org/wiki/Harshad_number#Consecutive_harshad_numbers">Harshad number</a>.
%H A330933 Brad Wilson, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/35-2/wilson.pdf">Construction of 2n consecutive n-Niven numbers</a>, Fibonacci Quarterly, Vol. 35, No. 2 (1997), pp. 122-128.
%e A330933 6222 is a term since 6222, 6223, 6224 and 6225 are all Niven numbers in base 2.
%t A330933 binNivenQ[n_] := Divisible[n, Total @ IntegerDigits[n, 2]]; bin = binNivenQ /@ Range[4]; seq = {}; Do[bin = Join[Rest[bin], {binNivenQ[k]}]; If[And @@ bin, AppendTo[seq, k - 3]], {k, 4, 10^6}]; seq
%o A330933 (Magma) f:=func<n|n mod &+Intseq(n,2) eq 0>; a:=[]; for k in [1..1400000] do if forall{m:m in [0..3]|f(k+m)} then Append(~a,k); end if; end for; a; // _Marius A. Burtea_, Jan 03 2020
%Y A330933 Cf. A049445, A141769, A328211, A328215, A330931, A330932.
%K A330933 nonn,base
%O A330933 1,1
%A A330933 _Amiram Eldar_, Jan 03 2020