

A298976


Base6 complementary numbers: n equals the product of the 6 complement (6d) of its base6 digits d.


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 base10 variant, which is the main entry for this family of sequences, and A298977 for the base7 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 = (63), therefore 3 is in the sequence.
Denoting xyz[6] the base6 expansion (i.e., x*6^2 + y*6 + z), we have:
10 = 14[6] = (61)*(64), therefore 10 is in the sequence.
18 = 30[6] = (63)*(60), therefore 18 is in the sequence.
80 = 212[6] = (62)*(61)*(62), 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*(60) is in the sequence.


PROG

(PARI) is(n, b=6)={n==prod(i=1, #n=digits(n, b), bn[i])}
(PARI) a(n)=if(n>5, a(n%3+3)*6^(n\31), [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: A210286 A275988 A177955 * A265487 A074893 A074178
Adjacent sequences: A298973 A298974 A298975 * A298977 A298978 A298979


KEYWORD

nonn,base,easy


AUTHOR

M. F. Hasler, Feb 09 2018


STATUS

approved



