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A135576 Numbers whose binary expansion has only the digit "1" as first, central and final digit. 7
1, 7, 21, 73, 273, 1057, 4161, 16513, 65793, 262657, 1049601, 4196353, 16781313, 67117057, 268451841, 1073774593, 4295032833, 17180000257, 68719738881, 274878431233, 1099512676353, 4398048608257, 17592190238721 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is essentially identical to A001576.

a(n) is the number whose binary representation is A135577(n), (See example). - Omar E. Pol, Nov 18 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

FORMULA

a(1)=1. If n>1 then a(n) = A001576(n-1).

G.f.: -x*(16*x^3-14*x^2+1) / ((x-1)*(2*x-1)*(4*x-1)). - Colin Barker, Sep 16 2013

EXAMPLE

--------------------------------------

n ........ a(n) ..... a(n) in base 2

--------------------------------------

1 .......... 1 ............ 1

2 .......... 7 ........... 111

3 ......... 21 .......... 10101

4 ......... 73 ......... 1001001

5 ........ 273 ........ 100010001

6 ....... 1057 ....... 10000100001

7 ....... 4161 ...... 1000001000001

8 ...... 16513 ..... 100000010000001

9 ...... 65793 .... 10000000100000001

10 .... 262657 ... 1000000001000000001

MATHEMATICA

nxt[n_]:=Module[{l=Floor[IntegerLength[n, 2]/2]}, FromDigits[Join[{1}, Table[0, {l}], {1}, Table[0, {l}], {1}], 2]]

NestList[nxt, 1, 25]  [From Harvey P. Dale, Dec 29 2010]

Join[{1}, LinearRecurrence[{7, -14, 8}, {7, 21, 73}, 30]] (* Harvey P. Dale, Mar 22 2015 *)

PROG

(PARI) a(n)=if(n--, 4^n+2^n+1, 1) \\ Charles R Greathouse IV, Dec 28 2012

CROSSREFS

Cf. A001576, A135577.

Sequence in context: A215494 A146533 A208534 * A153497 A146247 A241431

Adjacent sequences:  A135573 A135574 A135575 * A135577 A135578 A135579

KEYWORD

nonn,base,easy

AUTHOR

Omar E. Pol, Feb 24 2008, Dec 27 2008

STATUS

approved

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Last modified November 22 05:36 EST 2017. Contains 295076 sequences.