This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A047257 #63 Feb 13 2024 20:03:27
%S A047257 4,5,10,11,16,17,22,23,28,29,34,35,40,41,46,47,52,53,58,59,64,65,70,
%T A047257 71,76,77,82,83,88,89,94,95,100,101,106,107,112,113,118,119,124,125,
%U A047257 130,131,136,137,142,143,148,149
%N A047257 Numbers that are congruent to {4, 5} mod 6.
%C A047257 Equivalently, numbers m such that 2^m - m is divisible by 3. Indeed, for every prime p, there are infinitely many numbers m such that 2^m - m (A000325) is divisible by p, here are numbers m corresponding to p = 3. - _Bernard Schott_, Dec 10 2021
%C A047257 Numbers k for which A276076(k) and A276086(k) are multiples of nine. For a simple proof, consider the penultimate digit in the factorial and primorial base expansions of n, A007623 and A049345. - _Antti Karttunen_, Feb 08 2024
%D A047257 Michael Doob, The Canadian Mathematical Olympiad & L'Olympiade Mathématique du Canada 1969-1993, Canadian Mathematical Society & Société Mathématique du Canada, Problem 4, 1983, page 158, 1993.
%H A047257 David Lovler, <a href="/A047257/b047257.txt">Table of n, a(n) for n = 1..1000</a>
%H A047257 The IMO Compendium, <a href="https://imomath.com/othercomp/Can/CanMO83.pdf">Problem 4</a>, 15th Canadian Mathematical Olympiad 1983.
%H A047257 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%H A047257 <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%F A047257 a(n) = 4 + 6*floor(n/2) + n mod 2.
%F A047257 a(n) = 6*n-a(n-1)-3, with a(1)=4. - _Vincenzo Librandi_, Aug 05 2010
%F A047257 G.f.: ( x*(4+x+x^2) ) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F A047257 a(n) = 3*n - (-1)^n. - _Wesley Ivan Hurt_, Mar 20 2015
%F A047257 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(6*sqrt(3)) - log(2)/3. - _Amiram Eldar_, Dec 14 2021
%F A047257 E.g.f.: 1 + 3*x*exp(x) - exp(-x). - _David Lovler_, Aug 25 2022
%t A047257 Select[Range@ 150, 4 <= Mod[#, 6] <= 5 &] (* _Michael De Vlieger_, Mar 20 2015 *)
%t A047257 LinearRecurrence[{1,1,-1},{4,5,10},50] (* _Harvey P. Dale_, Oct 16 2017 *)
%o A047257 (Maxima) A047257(n):=4 + 6*floor(n/2) + mod(n,2)$ akelist(A047257(n),n,0,40); /* _Martin Ettl_, Oct 24 2012 */
%o A047257 (PARI) a(n) = 3*n - (-1)^n \\ _David Lovler_, Aug 25 2022
%Y A047257 Cf. A000325.
%Y A047257 Similar with: A299174 (p = 2), this sequence (p = 3), A349767 (p = 5).
%Y A047257 Cf. also A047227, A047235, A047246, A047247, A047270.
%Y A047257 Cf. A007623, A049345, A276076, A276086.
%K A047257 nonn,easy
%O A047257 1,1
%A A047257 _N. J. A. Sloane_