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A337449
The numbers k for which Lucas(k) are Niven numbers.
3
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
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
KEYWORD
nonn,base
AUTHOR
Marius A. Burtea, Sep 14 2020
STATUS
approved