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A352511 Starts of runs of 4 consecutive Catalan-Niven numbers (A352508). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 23:44 EDT 2022. Contains 357051 sequences. (Running on oeis4.)