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

144, 15630, 164862, 202761, 373788, 450189, 753183, 1403961, 1779105, 2588415, 2673774, 2814229, 2850880, 3009174, 3013722, 3045870, 3091023, 3702390, 3942519, 4042950, 4432128, 4725432, 4938348, 5718942, 5907312, 6268248, 6519615, 6592752, 6791379, 7095492, 8567802

Offset: 1

Author

Amiram Eldar, Mar 19 2022

Keywords

• nonn
• base

Comments

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

Examples

			144 is a term since 144, 145, 146 and 147 are all divisible by the sum of the digits in their Catalan representation:
    k  A014418(k)  A014420(k)  k/A014420(k)
  ---  ----------  ----------  ------------
  144      100210           4            36
  145      100211           5            29
  146      101000           2            73
  147      101001           3            49
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000108, A014418, A014420.

Subsequence of A352508, A352509 and A352510.

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

Programs

Mathematica

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]