# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a047406
Showing 1-1 of 1

%I A047406 #42 Sep 03 2022 08:50:11
%S A047406 4,6,12,14,20,22,28,30,36,38,44,46,52,54,60,62,68,70,76,78,84,86,92,
%T A047406 94,100,102,108,110,116,118,124,126,132,134,140,142,148,150,156,158,
%U A047406 164,166,172,174,180,182,188,190,196,198,204,206,212,214,220,222,228
%N A047406 Numbers that are congruent to {4, 6} mod 8.
%C A047406 In groups of four, add the odd and even numbers (4=1+3, 6=2+4; 12=5+7, 14=6+8; etc.). - _George E. Antoniou_, Dec 12 2001
%C A047406 The first 250 terms (4 through 998) are the 250 non-occurring Fibonacci number residues modulo 1000; i.e., if leading zeros are supplied as necessary for the terms having fewer than three digits, these are the 250 sets of three digits that never appear as the last three digits of a Fibonacci number. - _Jon E. Schoenfield_, Jul 05 2010
%H A047406 David Lovler, <a href="/A047406/b047406.txt">Table of n, a(n) for n = 1..1000</a>
%H A047406 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047406 a(n) = A042964(n)*2.
%F A047406 a(n) = (4*n - 1 - (-1)^n). - _Jon E. Schoenfield_, Jul 05 2010
%F A047406 a(n) = 8*n - a(n-1) - 6 (with a(1)=4). - _Vincenzo Librandi_, Aug 05 2010
%F A047406 G.f.: 2*x*(2+x+x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F A047406 From _Wesley Ivan Hurt_, May 18 2013: (Start)
%F A047406 a(n) = (8 * ceiling(n/2) - 4) * (n mod 2) + (8 * ceiling(n/2) - 2) * (n+1 mod 2).
%F A047406 a(n) = 8 * ceiling(n/2) - 3 + (-1)^n. (End)
%F A047406 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/16 - log(2)/8. - _Amiram Eldar_, Dec 19 2021
%F A047406 E.g.f.: 2*(1 + 2*x*exp(x) - cosh(x)). - _David Lovler_, Sep 02 2022
%e A047406 a(2) = 8*2 - 4 - 6 = 6;
%e A047406 a(3) = 8*3 - 6 - 6 = 12;
%e A047406 a(4) = 8*4 - 12 - 6 = 14.
%t A047406 Select[Range[230], MemberQ[{4, 6}, Mod[#, 8]] &] (* _Amiram Eldar_, Dec 19 2021 *)
%o A047406 (PARI) a(n)=4*n-1-(-1)^n \\ _Charles R Greathouse IV_, May 20 2013
%Y A047406 Union of A017113 and A017137.
%Y A047406 Cf. A042964.
%K A047406 nonn,easy
%O A047406 1,1
%A A047406 _N. J. A. Sloane_

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE