cp's OEIS Frontend

A098704 Decimal form of the binary numbers 10, 100010, 1000100010, 10001000100010, 100010001000100010,...

%I A098704 #37 Aug 30 2024 02:56:11
%S A098704 2,34,546,8738,139810,2236962,35791394,572662306,9162596898,
%T A098704 146601550370,2345624805922,37529996894754,600479950316066,
%U A098704 9607679205057058,153722867280912930,2459565876494606882
%N A098704 Decimal form of the binary numbers 10, 100010, 1000100010, 10001000100010, 100010001000100010,...
%C A098704 Decimal form of the hexadecimal numbers 2, 22, 222, 2222, 22222, 222222, ...; e.g., 2*16^0 + 2*16^1 = 2 + 32 = 34. - _Zerinvary Lajos_, Feb 01 2007
%C A098704 For n>0: A131852(a(n+1))=n and ABS(A131852(m))<n for m<a(n+1); a(n)=2*A131865(n-2). - _Reinhard Zumkeller_, Jul 22 2007
%C A098704 Third quadrisection of A115451. - _Klaus Purath_, Mar 14 2021
%H A098704 Harvey P. Dale, <a href="/A098704/b098704.txt">Table of n, a(n) for n = 2..832</a>
%H A098704 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (17,-16).
%F A098704 lim_{n -> infinity} a(n)/a(n-k) = 2^(4*(n-k)).
%F A098704 2*Sum_{k=0..n} 16^k = 2*(16^(n+1) - 1)/15.
%F A098704 From _Klaus Purath_, Mar 14 2021: (Start)
%F A098704 a(n) = (2^(4*n-3)-2)/15.
%F A098704 a(n) = 17*a(n-1) - 16*a(n-2).
%F A098704 a(n) = 16*a(n-1) + 2.
%F A098704 a(n) = 2*16^(n-2) + a(n-1).
%F A098704 a(n) = 2*A131865(n-2). (End)
%t A098704 s=0;lst={};Do[s+=2^n;AppendTo[lst, s], {n, 1, 2*5!, 4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 07 2008 *)
%t A098704 FromDigits[#,2]&/@Table[Join[PadRight[{},4n,{1,0,0,0}],{1,0}],{n,0,20}] (* _Harvey P. Dale_, Apr 06 2020 *)
%o A098704 (PARI) for(n=0,20,print(2*sum(k=0,n,2^(4*k))))
%o A098704 for(k=0,20,print(2*(1-16^(k+1))/-15))
%K A098704 nonn,base,easy
%O A098704 2,1
%A A098704 _Simone Severini_, Oct 26 2004
%E A098704 More terms from _Ray Chandler_, Nov 02 2004
%E A098704 More terms from _Vladimir Joseph Stephan Orlovsky_, Nov 07 2008