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%I #14 Feb 27 2019 12:30:34
%S 12,84,120,588,840,4116,5880,28812,41160,201684,288120,1411788,
%T 2016840,9882516,14117880,69177612,98825160,484243284,691776120,
%U 3389702988,4842432840,23727920916,33897029880,166095446412,237279209160,1162668124884,1660954464120
%N Base-7 complementary numbers: n equals the product of the 7 complement (7-d) of its base-7 digits d.
%C 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.
%C See A294090 for the base-10 variant, which is the main entry, and A298976 for the base-6 variant.
%H Colin Barker, <a href="/A298977/b298977.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 7).
%F a(n+2) = 7 a(n) for all n >= 1.
%F From _Colin Barker_, Feb 10 2018: (Start)
%F G.f.: 12*x*(1 + 7*x + 3*x^2) / (1 - 7*x^2).
%F a(n) = 12*7^(n/2) for n>1 and even.
%F a(n) = 120*7^((n-3)/2) for n>1 and odd.
%F (End)
%e Denoting xyz[7] the base-7 expansion (of n = x*7^2 + y*7 + z), we have:
%e 12 = 15[7] = (7-1)*(7-5), therefore 12 is in the sequence.
%e 84 = 150[7] = (7-1)*(7-5)*(7-0), therefore 84 is in the sequence.
%e 120 = 231[7] = (7-2)*(7-3)*(7-1), therefore 120 is in the sequence.
%e 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*(7-0) is in the sequence.
%o (PARI) is(n,b=7)={n==prod(i=1,#n=digits(n,b),b-n[i])}
%o (PARI) a(n)=[84,120][n%2+(n>1)]*7^(n\2-1)
%o (PARI) Vec(12*x*(1 + 7*x + 3*x^2) / (1 - 7*x^2) + O(x^60)) \\ _Colin Barker_, Feb 10 2018
%Y Cf. A294090, A298976.
%K nonn,base,easy
%O 1,1
%A _M. F. Hasler_, Feb 09 2018
%E More terms from _Colin Barker_, Feb 10 2018
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