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 A328205 #15 Jan 05 2025 19:51:41
%S A328205 1,8,26,35,90,122,244,245,300,384,440,510,722,804,844,845,935,944,984,
%T A328205 1014,1079,1224,1232,1444,1445,1518,1584,1589,1727,1728,1736,1770,
%U A328205 1880,2159,2184,2232,2240,2528,2540,2650,2820,2980,3032,3263,3640,4199,4328,4848
%N A328205 Numbers m such that m and m+1 are consecutive factorial base Niven numbers (A118363).
%C A328205 Dahlenberg & Edgar proved that this sequence is infinite.
%H A328205 Amiram Eldar, <a href="/A328205/b328205.txt">Table of n, a(n) for n = 1..10000</a>
%H A328205 Paul Dahlenberg and Tom Edgar, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Abstracts/56-2/dalenberg.pdf">Consecutive factorial base Niven numbers</a>, Fibonacci Quarterly, Vol. 56, No. 2 (2018), pp. 163-166; <a href="https://web.archive.org/web/20211018191809/https://community.plu.edu/~edgartj/consecutivefactniven.pdf">alternative link</a>.
%e A328205 8 is in the sequence since both 8 and 9 are in A118363. A034968(8) = 2 is a divisor of 8 and A034968(9) = 3 is a divisor of 9.
%t A328205 sf[n_] := Module[{s = 0, i = 2, k = n}, While[k > 0, k = Floor[n/i!]; s = s + (i - 1)*k; i++]; n - s]; fnQ[n_] := Divisible[n, sf[n]]; aQ[n_] := AllTrue[n + Range[0, 1], fnQ]; Select[Range[5000], aQ] (* after _Jean-François Alcover_ at A034968 *)
%Y A328205 Cf. A007623, A034968, A118363.
%K A328205 nonn,base
%O A328205 1,2
%A A328205 _Amiram Eldar_, Oct 07 2019