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

Author

Amiram Eldar, Mar 12 2022

Keywords

• nonn
• base

Comments

Numbers k such that A265744(k) | k.

All the positive Pell numbers (A000129) are terms.

Examples

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

Links

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

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.

Programs

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]