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

Author

Omar E. Pol, Feb 24 2008

Keywords

• nonn
• base
• easy

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

Examples

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

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).

Crossrefs

Cf. A001576, A135577.

Subsequence of A006995.

Programs

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 *)

PARI

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

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