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A098704
Decimal form of the binary numbers 10, 100010, 1000100010, 10001000100010, 100010001000100010,...
5
2, 34, 546, 8738, 139810, 2236962, 35791394, 572662306, 9162596898, 146601550370, 2345624805922, 37529996894754, 600479950316066, 9607679205057058, 153722867280912930, 2459565876494606882
OFFSET
2,1
COMMENTS
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
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
Third quadrisection of A115451. - Klaus Purath, Mar 14 2021
FORMULA
lim_{n -> infinity} a(n)/a(n-k) = 2^(4*(n-k)).
2*Sum_{k=0..n} 16^k = 2*(16^(n+1) - 1)/15.
From Klaus Purath, Mar 14 2021: (Start)
a(n) = (2^(4*n-3)-2)/15.
a(n) = 17*a(n-1) - 16*a(n-2).
a(n) = 16*a(n-1) + 2.
a(n) = 2*16^(n-2) + a(n-1).
a(n) = 2*A131865(n-2). (End)
MATHEMATICA
s=0; lst={}; Do[s+=2^n; AppendTo[lst, s], {n, 1, 2*5!, 4}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 07 2008 *)
FromDigits[#, 2]&/@Table[Join[PadRight[{}, 4n, {1, 0, 0, 0}], {1, 0}], {n, 0, 20}] (* Harvey P. Dale, Apr 06 2020 *)
PROG
(PARI) for(n=0, 20, print(2*sum(k=0, n, 2^(4*k))))
for(k=0, 20, print(2*(1-16^(k+1))/-15))
CROSSREFS
Sequence in context: A218432 A071799 A273052 * A119298 A045585 A092883
KEYWORD
nonn,base,easy
AUTHOR
Simone Severini, Oct 26 2004
EXTENSIONS
More terms from Ray Chandler, Nov 02 2004
More terms from Vladimir Joseph Stephan Orlovsky, Nov 07 2008
STATUS
approved