A352510 Starts of runs of 3 consecutive Catalan-Niven numbers (A352508).

4, 55, 144, 145, 511, 2943, 6950, 7734, 9470, 9750, 15630, 15631, 35034, 35464, 41590, 41986, 64735, 68523, 68870, 77510, 81150, 90958, 106063, 118264, 119043, 135970, 139403, 163188, 164862, 164863, 171346, 181510, 200759, 202761, 202762, 208024, 209230, 209586

Offset: 1

Author

Amiram Eldar, Mar 19 2022

Keywords

• nonn
• base

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000108, A014418, A014420.

Subsequence of A352508 and A352509.

A352511 is a subsequence.

Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091, A352109, A352322, A352344.

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[30, 3]