A047258 -id:A047258 - cp's OEIS frontend

A113867 a(n) = a(n-1) + 2^(A047258(n)) for n>1, a(1)=1.

1, 17, 49, 113, 1137, 3185, 7281, 72817, 203889, 466033, 4660337, 13048945, 29826161, 298261617, 835132529, 1908874353, 19088743537, 53448481905, 122167958641, 1221679586417, 3420702841969, 7818749353073, 78187493530737

Offset: 1

Artur Jasinski, Jan 27 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A099974, A112627, A080355, A080567, A099969, A099970, A099971.

CoefficientList[Series[(1 + 16 x + 32 x^2) / ((-1 + x) (- 1 + 4 x) (1 + 4 x + 16 x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, May 20 2013 *)

G.f.: x*(1+16*x+32*x^2)/((-1+x)*(-1+4*x)*(1+4*x+16*x^2)). - Vaclav Kotesovec, Nov 28 2012

Edited with better definition and offset corrected by Omar E. Pol, Jan 08 2009

A047245 Numbers that are congruent to {1, 2, 3} mod 6.

Original entry on oeis.org

1, 2, 3, 7, 8, 9, 13, 14, 15, 19, 20, 21, 25, 26, 27, 31, 32, 33, 37, 38, 39, 43, 44, 45, 49, 50, 51, 55, 56, 57, 61, 62, 63, 67, 68, 69, 73, 74, 75, 79, 80, 81, 85, 86, 87, 91, 92, 93, 97, 98, 99, 103, 104, 105, 109, 110, 111, 115, 116, 117, 121, 122, 123

Offset: 1

N. J. A. Sloane

a(k)^m is a term iff {a(k) is odd and m is a nonnegative integer} or {m is in A004273}. - Jerzy R Borysowicz, May 08 2023

David Lovler, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A047240, A047244, A047258 (complement).

[2*n-3+((2*n-3) mod 3) : n in [1..100]]; // Wesley Ivan Hurt, Apr 13 2015

A047245:=n->2*n-3+((2*n-3) mod 3): seq(A047245(n), n=1..100); # Wesley Ivan Hurt, Apr 13 2015

Select[Range[0, 200], Mod[#, 6] == 1 || Mod[#, 6] == 2 || Mod[#, 6] == 3 &] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)
Flatten[Table[{6n + 1, 6n + 2, 6n + 3}, {n, 0, 19}]] (* Alonso del Arte, Jul 07 2011 *)
Select[Range[0, 200], MemberQ[{1, 2, 3}, Mod[#, 6]] &] (* Vincenzo Librandi, Apr 14 2015 *)

a(n) = 3*floor((n-1)/3) + n; \\ David Lovler, Aug 03 2022

From Johannes W. Meijer, Jun 07 2011: (Start)
a(n) = ceiling(n/3) + ceiling((n-1)/3) + ceiling((n-2)/3) + 3*ceiling((n-3)/3).
G.f.: x*(1+x+x^2+3*x^3)/((x-1)^2*(x^2+x+1)). (End)
a(n) = 3*floor((n-1)/3) + n. - Gary Detlefs, Dec 22 2011
From Wesley Ivan Hurt, Apr 13 2015: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = 2*n-3 + ((2*n-3) mod 3). (End)
From Wesley Ivan Hurt, Jun 13 2016: (Start)
a(n) = 2*n - 2 - cos(2*n*Pi/3) + sin(2*n*Pi/3)/sqrt(3).
a(3k) = 6k-3, a(3k-1) = 6k-4, a(3k-2) = 6k-5. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (9-2*sqrt(3))*Pi/36 + log(2+sqrt(3))/(2*sqrt(3)) - log(2)/6. - Amiram Eldar, Dec 14 2021

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A113867 a(n) = a(n-1) + 2^(A047258(n)) for n>1, a(1)=1.

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A047245 Numbers that are congruent to {1, 2, 3} mod 6.

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