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 A352510 #8 Apr 01 2022 11:38:21
%S A352510 4,55,144,145,511,2943,6950,7734,9470,9750,15630,15631,35034,35464,
%T A352510 41590,41986,64735,68523,68870,77510,81150,90958,106063,118264,119043,
%U A352510 135970,139403,163188,164862,164863,171346,181510,200759,202761,202762,208024,209230,209586
%N A352510 Starts of runs of 3 consecutive Catalan-Niven numbers (A352508).
%H A352510 Amiram Eldar, <a href="/A352510/b352510.txt">Table of n, a(n) for n = 1..10000</a>
%e A352510 4 is a term since 4, 5 and 6 are all Catalan-Niven numbers: the Catalan representation of 4, A014418(20) = 20, has the sum of digits 2+0 = 2 and 4 is divisible by 2, the Catalan representation of 5, A014418(5) = 100, has the sum of digits 1+0+0 = 1 and 5 is divisible by 1, and the Catalan representation of 6, A014418(6) = 101, has the sum of digits 1+0+1 = 2 and 6 is divisible by 2.
%t A352510 c[n_] := c[n] = CatalanNumber[n]; catNivQ[n_] := Module[{s = {}, m = n, i}, While[m > 0, i = 1; While[c[i] <= m, i++]; i--; m -= c[i]; AppendTo[s, i]]; Divisible[n, Plus @@ IntegerDigits[Total[4^(s - 1)], 4]]]; seq[count_, nConsec_] := Module[{cn = catNivQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ cn, c++; AppendTo[s, k - nConsec]]; cn = Join[Rest[cn], {catNivQ[k]}]; k++]; s]; seq[30, 3]
%Y A352510 Cf. A000108, A014418, A014420.
%Y A352510 Subsequence of A352508 and A352509.
%Y A352510 A352511 is a subsequence.
%Y A352510 Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322, A352344.
%K A352510 nonn,base
%O A352510 1,1
%A A352510 _Amiram Eldar_, Mar 19 2022