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

1,2

Comments

Numbers k such that k | A000931(k).

Links

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

Example

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.

Mathematica

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

Prog

(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); }

Crossrefs

Cf. A000931.

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

Sequence in context: A131475 A239363 A045541 * A234639 A358000 A275674

Adjacent sequences: A372895 A372896 A372897 * A372899 A372900 A372901

Keyword

nonn,easy

Author

Amiram Eldar, May 16 2024

Status

approved