

A298977


Base7 complementary numbers: n equals the product of the 7 complement (7d) of its base7 digits d.


3



12, 84, 120, 588, 840, 4116, 5880, 28812, 41160, 201684, 288120, 1411788, 2016840, 9882516, 14117880, 69177612, 98825160, 484243284, 691776120, 3389702988, 4842432840, 23727920916, 33897029880, 166095446412, 237279209160, 1162668124884, 1660954464120
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OFFSET

1,1


COMMENTS

The only primitive terms of the sequence, i.e., not equal to 7 times a smaller term, are a(1) = 12 and a(3) = 120.
See A294090 for the base10 variant, which is the main entry, and A298976 for the base6 variant.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0, 7).


FORMULA

a(n+2) = 7 a(n) for all n >= 1.
From Colin Barker, Feb 10 2018: (Start)
G.f.: 12*x*(1 + 7*x + 3*x^2) / (1  7*x^2).
a(n) = 12*7^(n/2) for n>1 and even.
a(n) = 120*7^((n3)/2) for n>1 and odd.
(End)


EXAMPLE

Denoting xyz[7] the base7 expansion (of n = x*7^2 + y*7 + z), we have:
12 = 15[7] = (71)*(75), therefore 12 is in the sequence.
84 = 150[7] = (71)*(75)*(70), therefore 84 is in the sequence.
120 = 231[7] = (72)*(73)*(71), therefore 120 is in the sequence.
Since the expansion of 7*x in base 7 is that of x with a 0 appended, if x is in the sequence, then 7*x = x*(70) is in the sequence.


PROG

(PARI) is(n, b=7)={n==prod(i=1, #n=digits(n, b), bn[i])}
(PARI) a(n)=[84, 120][n%2+(n>1)]*7^(n\21)
(PARI) Vec(12*x*(1 + 7*x + 3*x^2) / (1  7*x^2) + O(x^60)) \\ Colin Barker, Feb 10 2018


CROSSREFS

Cf. A294090, A298976.
Sequence in context: A165127 A213347 A075476 * A213784 A085409 A303916
Adjacent sequences: A298974 A298975 A298976 * A298978 A298979 A298980


KEYWORD

nonn,base,easy


AUTHOR

M. F. Hasler, Feb 09 2018


EXTENSIONS

More terms from Colin Barker, Feb 10 2018


STATUS

approved



