A135576 Numbers whose binary expansion has only the digit "1" as first, central and final digit.

1, 7, 21, 73, 273, 1057, 4161, 16513, 65793, 262657, 1049601, 4196353, 16781313, 67117057, 268451841, 1073774593, 4295032833, 17180000257, 68719738881, 274878431233, 1099512676353, 4398048608257, 17592190238721

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] (* 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.

Subsequence of A006995.

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

Status

approved