A352511 - OEIS

%I #9 Apr 01 2022 11:38:26

%S 144,15630,164862,202761,373788,450189,753183,1403961,1779105,2588415,

%T 2673774,2814229,2850880,3009174,3013722,3045870,3091023,3702390,

%U 3942519,4042950,4432128,4725432,4938348,5718942,5907312,6268248,6519615,6592752,6791379,7095492,8567802

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

%C Conjecture: There are no runs of 5 consecutive Catalan-Niven numbers (checked up to 10^9).

%H Amiram Eldar, <a href="/A352511/b352511.txt">Table of n, a(n) for n = 1..1000</a>

%e 144 is a term since 144, 145, 146 and 147 are all divisible by the sum of the digits in their Catalan representation:

%e     k  A014418(k)  A014420(k)  k/A014420(k)

%e   ---  ----------  ----------  ------------

%e   144      100210           4            36

%e   145      100211           5            29

%e   146      101000           2            73

%e   147      101001           3            49

%t 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 Cf. A000108, A014418, A014420.

%Y Subsequence of A352508, A352509 and A352510.

%Y Similar sequences: A141769, A328211, A328207, A328215, A330933, A331824, A334311, A342429, A344344, A352092, A352110, A352345.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Mar 19 2022