|
| |
|
|
A195744
|
|
a(n) = 15*2^(n+1) + 1.
|
|
11
|
|
|
|
31, 61, 121, 241, 481, 961, 1921, 3841, 7681, 15361, 30721, 61441, 122881, 245761, 491521, 983041, 1966081, 3932161, 7864321, 15728641, 31457281, 62914561, 125829121, 251658241, 503316481, 1006632961, 2013265921, 4026531841, 8053063681, 16106127361
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
Binary numbers of form 1111(0^n)1 where n is the index and number of 0's.
Base 10 numbers of this sequence always end in 1.
An Engel expansion of 1/15 to the base 2 as defined in A181565, with the associated series expansion 1/15 = 2/31 + 2^2/(31*61) + 2^3/(31*61*121) + 2^4/(31*61*121*241) + .... - Peter Bala, Oct 29 2013
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).
|
|
|
FORMULA
|
a(n) = A052996(n+3) + A164094(n+2).
From Bruno Berselli, Sep 23 2011: (Start)
G.f.: (31-32*x)/(1-3*x+2*x^2).
a(n) = 2*a(n-1)-1.
a(n) = A110286(n+1)+1 = A128470(2^n). (End)
|
|
|
EXAMPLE
|
First few terms in binary are 11111, 111101, 1111001, 11110001, 111100001.
|
|
|
PROG
|
(MAGMA) [15*2^(n+1) + 1: n in [0..30]]; // Vincenzo Librandi, Sep 24 2011
(PARI) a(n)=30*2^n+1 \\ Charles R Greathouse IV, Oct 07 2015
|
|
|
CROSSREFS
|
Cf. A052996, A164094. A020737, A083575, A083683, A083686, A083705, A168596, A181565.
Sequence in context: A078562 A054804 A128470 * A331324 A326896 A132230
Adjacent sequences: A195741 A195742 A195743 * A195745 A195746 A195747
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Brad Clardy, Sep 23 2011
|
|
|
EXTENSIONS
|
Corrected by Arkadiusz Wesolowski, Sep 23 2011
|
|
|
STATUS
|
approved
|
| |
|
|
