A298976 Base-6 complementary numbers: n equals the product of the 6 complement (6-d) of its base-6 digits d.

3, 10, 18, 60, 80, 108, 360, 480, 648, 2160, 2880, 3888, 12960, 17280, 23328, 77760, 103680, 139968, 466560, 622080, 839808, 2799360, 3732480, 5038848, 16796160, 22394880, 30233088, 100776960, 134369280, 181398528, 604661760, 806215680, 1088391168

Offset

1,1

Comments

The only primitive terms of the sequence, i.e., not equal to 6 times a smaller term, are a(1) = 3, a(2) = 10 and a(5) = 80.

See A294090 for the base-10 variant, which is the main entry for this family of sequences, and A298977 for the base-7 variant.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,6).

Formula

a(n+3) = 6 a(n) for all n >= 2.

G.f.: x*(3 + 10*x + 18*x^2 + 42*x^3 + 20*x^4) / (1 - 6*x^3). - Colin Barker, Feb 09 2018

Example

3 = (6-3), therefore 3 is in the sequence.
Denoting xyz[6] the base-6 expansion (i.e., x*6^2 + y*6 + z), we have:
10 = 14[6] = (6-1)*(6-4), therefore 10 is in the sequence.
18 = 30[6] = (6-3)*(6-0), therefore 18 is in the sequence.
80 = 212[6] = (6-2)*(6-1)*(6-2), therefore 80 is in the sequence.
Since the expansion of 6*x in base 6 is that of x with a 0 appended, if x is in the sequence, then 6*x = x*(6-0) is in the sequence.

Prog

(PARI) is(n, b=6)={n==prod(i=1, #n=digits(n, b), b-n[i])}
(PARI) a(n)=if(n>5, a(n%3+3)*6^(n\3-1), [3, 10, 18, 60, 80][n])
(PARI) Vec(x*(3 + 10*x + 18*x^2 + 42*x^3 + 20*x^4) / (1 - 6*x^3) + O(x^60)) \\ Colin Barker, Feb 09 2018

Crossrefs

Cf. A294090, A298977.

Sequence in context: A275988 A177955 A372608 * A265487 A074893 A074178

Adjacent sequences: A298973 A298974 A298975 * A298977 A298978 A298979

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2018

Status

approved