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A228081 a(n) = 64^n + 1. 12
2, 65, 4097, 262145, 16777217, 1073741825, 68719476737, 4398046511105, 281474976710657, 18014398509481985, 1152921504606846977, 73786976294838206465, 4722366482869645213697, 302231454903657293676545, 19342813113834066795298817, 1237940039285380274899124225 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
These numbers can be written as the sum of two relatively prime squares and also as the sum of two relatively prime cubes (i.e., 2^(6*n) + 1 = (2^(3*n))^2 + 1^2 = (2^(2*n))^3 + 1^3).
LINKS
Arkadiusz Wesolowski, Table of n, a(n) for n = 0..100
FORMULA
a(n) = 64*a(n-1) - 63.
a(n) = A089357(n) + 1 = 2^A008588(n) + 1.
G.f.: (2 - 65*x)/((1 - x)*(1 - 64*x)).
E.g.f.: e^x + e^(64*x).
EXAMPLE
a(2) = 64^2 + 1 = 4097.
MATHEMATICA
Table[64^n + 1, {n, 0, 15}]
LinearRecurrence[{65, -64}, {2, 65}, 20] (* Harvey P. Dale, Jul 17 2020 *)
PROG
(Magma) [64^n+1 : n in [0..15]]
(PARI) for(n=0, 15, print1(64^n+1, ", "))
CROSSREFS
Cf. A000051 (2^n + 1), A052539 (4^n + 1), A062395 (8^n + 1).
Sequence in context: A199145 A198665 A185029 * A214366 A220596 A326253
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified May 22 13:22 EDT 2024. Contains 372755 sequences. (Running on oeis4.)