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Write n in binary n times and concatenate (see example). a(n) is the decimal equivalent.
2

%I #28 Jun 15 2021 13:41:56

%S 1,10,63,2340,23405,224694,2097151,2290649224,41231686041,

%T 733007751850,12900936432571,225179981368524,3903119677054429,

%U 67253754435399406,1152921504606846975,623961713349486025654800,21214698253882524872263217,718803893778607901554330194

%N Write n in binary n times and concatenate (see example). a(n) is the decimal equivalent.

%H Alois P. Heinz, <a href="/A162473/b162473.txt">Table of n, a(n) for n = 1..369</a>

%F a(n) = n * (2^(A070939(n)*n) - 1) / (2^(A070939(n)) - 1). - _Maxim Skorohodov_, Oct 26 2020

%e The binary representations of the first few terms are 1, 1010, 111111, 100100100100, 101101101101101.

%p A070939 := proc(n) max(1, ilog2(n)+1) ; end: A162473 := proc(n) local bid,a062383; bid := A070939(n) ; a062383 := 2^bid ; n*(a062383^n-1)/(a062383-1) ; end: seq(A162473(n),n=1..30) ; # _R. J. Mathar_, Jul 06 2009

%p # second Maple program:

%p a:= n-> Bits[Join](map(x-> x[], [Bits[Split](n)$n])):

%p seq(a(n), n=1..30); # _Alois P. Heinz_, Oct 26 2020

%t Table[FromDigits[Flatten[Table[IntegerDigits[n,2],{n}]],2],{n,20}] (* _Harvey P. Dale_, Jun 15 2021 *)

%Y Cf. A007088, A070939, A162472.

%K base,nonn

%O 1,2

%A _Leroy Quet_, Jul 04 2009

%E More terms from _R. J. Mathar_, Jul 06 2009