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

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Last modified December 7 22:29 EST 2019. Contains 329850 sequences. (Running on oeis4.)