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A352511 Starts of runs of 4 consecutive Catalan-Niven numbers (A352508).

%I A352511 #9 Apr 01 2022 11:38:26
%S A352511 144,15630,164862,202761,373788,450189,753183,1403961,1779105,2588415,
%T A352511 2673774,2814229,2850880,3009174,3013722,3045870,3091023,3702390,
%U A352511 3942519,4042950,4432128,4725432,4938348,5718942,5907312,6268248,6519615,6592752,6791379,7095492,8567802
%N A352511 Starts of runs of 4 consecutive Catalan-Niven numbers (A352508).
%C A352511 Conjecture: There are no runs of 5 consecutive Catalan-Niven numbers (checked up to 10^9).
%H A352511 Amiram Eldar, <a href="/A352511/b352511.txt">Table of n, a(n) for n = 1..1000</a>
%e A352511 144 is a term since 144, 145, 146 and 147 are all divisible by the sum of the digits in their Catalan representation:
%e A352511     k  A014418(k)  A014420(k)  k/A014420(k)
%e A352511   ---  ----------  ----------  ------------
%e A352511   144      100210           4            36
%e A352511   145      100211           5            29
%e A352511   146      101000           2            73
%e A352511   147      101001           3            49
%t A352511 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[5, 4]
%Y A352511 Cf. A000108, A014418, A014420.
%Y A352511 Subsequence of A352508, A352509 and A352510.
%Y A352511 Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345.
%K A352511 nonn,base
%O A352511 1,1
%A A352511 _Amiram Eldar_, Mar 19 2022