A352342 - OEIS

A352342

Lazy-Pell-Niven numbers: numbers that are divisible by the sum of the digits in their maximal (or lazy) representation in terms of the Pell numbers (A352339).

1, 2, 4, 9, 12, 15, 20, 24, 25, 28, 30, 35, 40, 48, 50, 54, 56, 60, 63, 64, 70, 72, 78, 84, 88, 91, 96, 102, 115, 120, 136, 144, 160, 162, 168, 180, 182, 184, 189, 207, 209, 210, 216, 217, 234, 246, 256, 261, 270, 304, 306, 308, 315, 320, 328, 333, 350, 352, 357

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OFFSET

1,2

COMMENTS

Numbers k such that A352340(k) | k.

LINKS

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

EXAMPLE

4 is a term since its maximal Pell representation, A352339(4) = 11, has the sum of digits A352340(4) = 1+1 = 2 and 4 is divisible by 2.

MATHEMATICA

pell[1] = 1; pell[2] = 2; pell[n_] := pell[n] = 2*pell[n - 1] + pell[n - 2]; pellp[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[pell[k] <= m, k++]; k--; AppendTo[s, k]; m -= pell[k]; k = 1]; IntegerDigits[Total[3^(s - 1)], 3]]; q[n_] := Module[{v = pellp[n]}, nv = Length[v]; i = 1; While[i <= nv - 2, If[v[[i]] > 0 && v[[i + 1]] == 0 && v[[i + 2]] < 2, v[[i ;; i + 2]] += {-1, 2, 1}; If[i > 2, i -= 3]]; i++]; i = Position[v, _?(# > 0 &)]; Divisible[n, Plus @@ v[[i[[1, 1]] ;; -1]]]]; Select[Range[300], q]

CROSSREFS

Cf. A352339, A352340.

Subsequences: A352343, A352344, A352345.

Sequence in context: A096186 A359817 A175041 * A298823 A219114 A182859

Adjacent sequences: A352339 A352340 A352341 * A352343 A352344 A352345

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Mar 12 2022

STATUS

approved