

A228081


a(n) = 64^n + 1.


12



2, 65, 4097, 262145, 16777217, 1073741825, 68719476737, 4398046511105, 281474976710657, 18014398509481985, 1152921504606846977, 73786976294838206465, 4722366482869645213697, 302231454903657293676545, 19342813113834066795298817, 1237940039285380274899124225
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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



FORMULA

a(n) = 64*a(n1)  63.
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



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



