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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)
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..175
Guo-Niu Han, Enumeration of Standard Puzzles
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).
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FORMULA
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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]
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MAPLE
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spec := [S, {S=Union(Sequence(Union(Z, Z, Z, Z)), Sequence(Z))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Table[4^n + 1, {n, 0, 25}]
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PROG
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(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
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CROSSREFS
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Cf. A000051, A034472, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600 - A074624.
Sequence in context: A150012 A150013 A123166 * A008932 A167809 A062881
Adjacent sequences: A052536 A052537 A052538 * A052540 A052541 A052542
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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