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A363789 a(n) is the smallest primitive binary Niven number (A363787) whose binary representation is ending with n zeros.

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%I A363789 #6 Jun 24 2023 13:22:39
%S A363789 1,6,60,2040,1048560,137438953440,1180591620717411303360,
%T A363789 43556142965880123323311949751266331066240,
%U A363789 29642774844752946028434172162224104410437116074403984394101141506025761187823360
%N A363789 a(n) is the smallest primitive binary Niven number (A363787) whose binary representation is ending with n zeros.
%C A363789 The least term k of A363787 such that A007814(k) = n.
%C A363789 Also, the least binary Niven number (A049445) with a binary weight (A000120) that equals 2^n.
%C A363789 The next term, a(9) = 6.864... * 10^156, is too long to include in the Data section.
%H A363789 Amiram Eldar, <a href="/A363789/b363789.txt">Table of n, a(n) for n = 0..11</a>
%F A363789 a(n) = (2^(2^n)-1) * 2^n = A066524(2^n).
%F A363789 a(n) = A143115(2^n).
%t A363789 a[n_] := (2^(2^n)-1) * 2^n; Array[a, 9, 0]
%o A363789 (PARI) a(n) = (2^(2^n)-1) * 2^n;
%Y A363789 Subsequence of A049445, A143115 and A363787.
%Y A363789 Cf. A000120, A007814, A066524, A358256 (decimal analog).
%K A363789 nonn,easy,base
%O A363789 0,2
%A A363789 _Amiram Eldar_, Jun 22 2023