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A144864
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A144863, read as binary numbers, converted to base 10.
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2
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1, 21, 341, 5461, 87381, 1398101, 22369621, 357913941, 5726623061, 91625968981, 1466015503701, 23456248059221, 375299968947541, 6004799503160661, 96076792050570581, 1537228672809129301
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| All numbers in this sequence for n>1 are congruent to 5 mod 16. [From Artur Jasinski, Sep 25 2008]
Contribution from Omar E. Pol, Sep 10 2011 (Start)
It appears that this is a bisection of A002450.
It appears that this is a bisection of A084241.
It appears that this is a bisection of A153497.
It appears that this is a bisection of A088556, if n>=2.
(End)
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..500
Index to sequences with linear recurrences with constant coefficients, signature (17,-16).
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FORMULA
| a(n) = 16^n/12-1/3; a(n) = 16*a(n-1)+5, a(1)=1. [From Artur Jasinski, Sep 25 2008]
G.f.: x*(1+4*x) / ( (16*x-1)*(x-1) ). - R. J. Mathar, Jan 06 2011
a(n)=b such that Integral_{x=-Pi/2..Pi/2} (-1)^(n+1)*2^(2*n-3)*(cos((2*n-1)*x))/(5/4+sin(x)) dx =c+b*ln(3). [From Francesco Daddi, Aug 02 2011]
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MATHEMATICA
| a = {}; k = {1}; Do[x = FromDigits[k, 2]; AppendTo[a, x]; AppendTo[k, 0]; AppendTo[k, 1]; PrependTo[k, 0]; PrependTo[k, 1], {n, 1, 100}]; a
Contribution from Artur Jasinski, Sep 25 2008: (Start)
Table[1/3 (-1 + 16^(n - 1)) + 16^(n - 1), {n, 1, 17}]
or
a = {}; k = 1; Do[AppendTo[a, k]; k = 16 k + 5, {n, 1, 17}]; a (End)
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PROG
| (MAGMA) [16^n/12-1/3: n in [1..20]]; // Vincenzo Librandi, Aug 03 2011
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CROSSREFS
| Cf. A056830, A094028, A135576, A144864.
Sequence in context: A166914 A020311 A068705 * A075921 A201878 A184289
Adjacent sequences: A144861 A144862 A144863 * A144865 A144866 A144867
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KEYWORD
| base,easy,nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Sep 23 2008
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