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%I #25 Mar 08 2024 16:39:49
%S 1,4,39,624,19999,1279936,163831935,41940975360,21473779384831,
%T 21989150090066944,45033779384457103359,184458360358736295358464,
%U 1511082888058767731576545279,24757582037954850514150117851136,811256448219704541647671061746057215
%N Concatenation of increasing number of alternating digits in base 2, starting with 1.
%H Harry J. Smith, <a href="/A065760/b065760.txt">Table of n, a(n) for n = 1..50</a>
%F a(n) = a(n-1) * 2^n if n is even, (a(n-1) + 1) * 2^n - 1 if n is odd. - _Franklin T. Adams-Watters_, Sep 18 2012
%e a(5) = 19999 is formed by appending 1 five times (11111) to a(4) in base 2: 100111000011111.
%p a:= proc(n) option remember; `if`(n=1, 1,
%p (t-> (a(n-1)+t)*2^n-t)(irem(n,2)))
%p end:
%p seq(a(n), n=1..17); # _Alois P. Heinz_, Mar 08 2024
%t With[{nn=20}, Table[FromDigits[Flatten[Take[Table[Table[If[EvenQ[n],0,1], {n}], {n,nn}], j]], 2], {j, nn}]] (* _Harvey P. Dale_, Sep 09 2012 *)
%o (PARI) baseI(x, b)= { local(d, e=0, f=1); while (x>0, d=x-10*(x\10); x\=10; e+=d*f; f*=b); return(e) } { c=1; for (n=1, 50, if (n==1, a=1; b=1, c=c*10 + 1; if (n%2, d=c, d=0); b=b*10^n + d; a=baseI(b, 2)); write("b065760.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 30 2009
%Y Decimal version of A065447.
%Y Cf. A065761.
%K base,easy,nonn
%O 1,2
%A _Lior Manor_, Nov 18 2001
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