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

1,1

Comments

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

Links

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

Example

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

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]

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.

Sequence in context: A252779 A238284 A249181 * A260861 A079658 A280024

Adjacent sequences: A352508 A352509 A352510 * A352512 A352513 A352514

Keyword

nonn,base

Author

Amiram Eldar, Mar 19 2022

Status

approved