A337449 The numbers k for which Lucas(k) are Niven numbers.

0, 1, 2, 3, 4, 6, 12, 18, 56, 81, 130, 225, 396, 637, 854, 2034, 4059, 4095, 5985, 7650, 21105, 31059, 41998, 46860, 83106, 114129, 120555, 150705, 201285, 287937, 338265, 359757, 475839, 512194, 583825, 606594, 627102, 717025, 877305, 922095, 991590, 1076355

Offset

1,3

Comments

For a(6) = 6, Lucas(6) = 18 and 18/digsum(18) = 2 is a prime number, so Lucas(6) is a Moran number (A001101).

For a(9) = 56, Lucas(56) = 505019158607 and 505019158607/digsum(505019158607) = 10745088481 is a prime number, so Lucas(56) is a Moran number.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..57

Example

Lucas(0) = 2 = A005349(2), so 0 is a term.
Lucas(1) = 1 = A005349(1), so 1 is a term.
Lucas(6) = 12 = A005349(11), so 6 is a term.
Lucas(12) = 322 = A005349(90), so 12 is a term.
Lucas(18) = 5778 = A005349(1013), so 18 is a term.

Mathematica

nivenQ[n_] := Divisible[n, Plus @@ IntegerDigits[n]]; Select[Range[6000], nivenQ[LucasL[#]] &] (* Amiram Eldar, Sep 15 2020 *)

Prog

(Magma) niven:=func<n|n mod &+Intseq(n) eq 0>; [k:k in [0..70000]|niven(Lucas(k))];
(PARI) isok(k) = my(l=real((2+quadgen(5))*quadgen(5)^k)); (l % sumdigits(l)) == 0; \\ Michel Marcus, Sep 15 2020
(Python)
A337449_list, k, p, q = [], 0, 2, 1
while k < 10**6:
    if p % sum(int(d) for d in str(p)) == 0:
        A337449_list.append(k)
    k += 1
    p, q = q, p+q # Chai Wah Wu, Sep 17 2020

Crossrefs

Cf. A000032, A139374, A001101, A005349, A337448.

Sequence in context: A118651 A206292 A129297 * A221846 A018343 A242459

Adjacent sequences: A337446 A337447 A337448 * A337450 A337451 A337452

Keyword

nonn,base

Author

Marius A. Burtea, Sep 14 2020

Status

approved