A352320 Pell-Niven numbers: numbers that are divisible by the sum of the digits in their minimal (or greedy) representation in terms of the Pell numbers (A317204).

1, 2, 4, 5, 6, 9, 10, 12, 14, 15, 18, 20, 24, 28, 29, 30, 33, 34, 36, 39, 40, 42, 44, 48, 50, 58, 60, 63, 64, 68, 70, 72, 82, 84, 87, 88, 90, 92, 96, 110, 111, 112, 115, 116, 120, 125, 126, 135, 140, 141, 144, 155, 164, 165, 168, 169, 170, 174, 180, 183, 184, 186

Offset

1,2

Comments

Numbers k such that A265744(k) | k.

All the positive Pell numbers (A000129) are terms.

Links

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

Example

6 is a term since its minimal Pell representation, A317204(6) = 101, has A265744(6) = 2 1's and 6 is divisible by 2.

Mathematica

pell[1] = 1; pell[2] = 2; pell[n_] := pell[n] = 2*pell[n - 1] + pell[n - 2]; q[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]; Divisible[n, Plus @@ IntegerDigits[ Total[3^(s - 1)], 3]]]; Select[Range[200], q]

Crossrefs

Cf. A000129, A265744, A317204.

Subsequences: A352321, A352322.

Similar sequences: A005349, A049445, A064150, A064438, A064481, A118363, A328208, A328212, A331085, A333426, A342726, A334308, A331728, A342426, A344341, A351714, A351719, A352089, A352107.

Sequence in context: A047435 A331085 A132791 * A352508 A125297 A194469

Adjacent sequences: A352317 A352318 A352319 * A352321 A352322 A352323

Keyword

nonn,base

Author

Amiram Eldar, Mar 12 2022

Status

approved