A372898 Numbers k that divide the k-th Padovan number.

1, 2, 4, 16, 25, 27, 59, 69, 101, 167, 173, 211, 223, 271, 307, 317, 347, 387, 422, 449, 463, 593, 599, 607, 634, 691, 694, 719, 809, 821, 829, 844, 853, 877, 883, 898, 926, 991, 997, 1097, 1117, 1151, 1163, 1181, 1197, 1198, 1231, 1319, 1369, 1388, 1451, 1453, 1481

Offset: 1

Author

Amiram Eldar, May 16 2024

Keywords

• nonn
• easy

Comments

Numbers k such that k | A000931(k).

Examples

			2 is a term since A000931(2) = 0 is divisible by 2.
27 is a term since A000931(27) = 351 = 13 * 27 is divisible by 27.
		

Links

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

Crossrefs

Cf. A000931.

Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).

Programs

Mathematica

With[{m = 1500}, Position[LinearRecurrence[{0, 1, 1}, {0, 0, 1}, m]/Range[m], _?IntegerQ] // Flatten]

PARI

lista(kmax) = {my(p1 = 0, p2 = 0, p3 = 1, p4); print1("1, 2, "); for(k = 4, kmax, p4 = p1 + p2; if(!(p4 % k), print1(k, ", ")); p1 = p2; p2 = p3; p3 = p4);}