# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a228081 Showing 1-1 of 1 %I A228081 #34 Sep 08 2022 08:46:05 %S A228081 2,65,4097,262145,16777217,1073741825,68719476737,4398046511105, %T A228081 281474976710657,18014398509481985,1152921504606846977, %U A228081 73786976294838206465,4722366482869645213697,302231454903657293676545,19342813113834066795298817,1237940039285380274899124225 %N A228081 a(n) = 64^n + 1. %C A228081 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). %H A228081 Arkadiusz Wesolowski, Table of n, a(n) for n = 0..100 %H A228081 Index entries for sequences related to sums of cubes %H A228081 Index entries for sequences related to sums of squares %H A228081 Index entries for linear recurrences with constant coefficients, signature (65,-64). %F A228081 a(n) = 64*a(n-1) - 63. %F A228081 a(n) = A089357(n) + 1 = 2^A008588(n) + 1. %F A228081 G.f.: (2 - 65*x)/((1 - x)*(1 - 64*x)). %F A228081 E.g.f.: e^x + e^(64*x). %e A228081 a(2) = 64^2 + 1 = 4097. %t A228081 Table[64^n + 1, {n, 0, 15}] %t A228081 LinearRecurrence[{65,-64},{2,65},20] (* _Harvey P. Dale_, Jul 17 2020 *) %o A228081 (Magma) [64^n+1 : n in [0..15]] %o A228081 (PARI) for(n=0, 15, print1(64^n+1, ", ")) %Y A228081 Cf. A000051 (2^n + 1), A052539 (4^n + 1), A062395 (8^n + 1). %K A228081 easy,nonn %O A228081 0,1 %A A228081 _Arkadiusz Wesolowski_, Aug 09 2013 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE