login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052539 4^n + 1. 55
2, 5, 17, 65, 257, 1025, 4097, 16385, 65537, 262145, 1048577, 4194305, 16777217, 67108865, 268435457, 1073741825, 4294967297, 17179869185, 68719476737, 274877906945, 1099511627777, 4398046511105, 17592186044417 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The sequence is a Lucas sequence V(P,Q) with P=5 and Q=4, so if n is a prime number, then V_n(5,4)-5 is divisible by n. The smallest pseudoprime q which divides V_q(5,4)-5 is 15.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..175

Guo-Niu Han, Enumeration of Standard Puzzles

Guo-Niu Han, Enumeration of Standard Puzzles [Cached copy]

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 470

Wikipedia, Lucas sequence: Specific names.

Index to sequences with linear recurrences with constant coefficients, signature (5,-4).

FORMULA

a(n) = 4^n+1.

a(n) = 4a(n-1) - 3 = 5a(n-1) - 4a(n-2).

G.f.: (2-5*x)/((1-4*x)*(1-x)).

E.g.f.: e^x+e^(4*x). - Mohammad K. Azarian, Jan 02 2009

MAPLE

spec := [S, {S=Union(Sequence(Union(Z, Z, Z, Z)), Sequence(Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);

A052539:=n->4^n + 1; seq(A052539(n), n=0..30); # Wesley Ivan Hurt, Jun 12 2014

MATHEMATICA

Table[4^n + 1, {n, 0, 25}]

PROG

(MAGMA) [4^n+1: n in [0..30] ]; // Vincenzo Librandi, Apr 30 2011

(PARI) a(n)=4^n+1 \\ Charles R Greathouse IV, Nov 20 2011

CROSSREFS

Cf. A000051, A034472, A034474, A062394, A034491, A062395, A062396, A062397, A007689, A063376, A063481, A074600-A074624, A034524, A178248, A228081.

Sequence in context: A150012 A150013 A123166 * A008932 A167809 A062881

Adjacent sequences:  A052536 A052537 A052538 * A052540 A052541 A052542

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 29 03:09 EST 2014. Contains 250479 sequences.