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 A047350 #39 Jun 22 2025 04:15:09
%S A047350 1,2,4,8,9,11,15,16,18,22,23,25,29,30,32,36,37,39,43,44,46,50,51,53,
%T A047350 57,58,60,64,65,67,71,72,74,78,79,81,85,86,88,92,93,95,99,100,102,106,
%U A047350 107,109,113,114,116,120,121,123,127,128,130,134,135,137,141
%N A047350 Numbers that are congruent to {1, 2, 4} mod 7.
%C A047350 a(n+1) = a(n) + (a(n) mod 7). - _Ben Paul Thurston_, Jan 09 2008
%C A047350 Also defined by: a(1)=1, and a(n) = smallest number larger than a(n-1) such that a(n)^3 - a(n-1)^3 is divisible by 7. - _Zak Seidov_, Apr 21 2009
%C A047350 Union of A047353 and A017029. - _R. J. Mathar_, Apr 28 2009
%C A047350 Indices of the even numbers in the Padovan sequence. - _Francesco Daddi_, Jul 31 2011
%C A047350 Euler's problem (see Link lines, English translation by David Zao): Finding the values of a so that the form a^3-1 is divisible by 7. The three residuals that remain after the division of any square by 7 are 1, 2 and 4. Hence the values are 7n+1, 7n+2, 7n+4. - _Bruno Berselli_, Oct 24 2012
%H A047350 Leonhard Euler, <a href="http://eulerarchive.maa.org/">The Euler Archive</a>, Theoremata circa divisores numerorum (E134), Novi Commentarii academiae scientiarum imperialis Petropolitanae, Volume 1 (1750), p. 40 (Theorem II, example 2).
%H A047350 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047350 From _R. J. Mathar_, Apr 28 2009: (Start)
%F A047350 G.f.: x*(1 + x + 2*x^2 + 3*x^3)/((1 + x + x^2)*(x-1)^2).
%F A047350 a(n) = a(n-1) + a(n-3) - a(n-4) for n > 4.
%F A047350 a(n) = a(n-3) + 7 for n > 3. (End)
%F A047350 From _Wesley Ivan Hurt_, Jun 13 2016: (Start)
%F A047350 a(n) = (21*n - 21 - 6*cos(2*n*Pi/3) + 4*sqrt(3)*sin(2*n*Pi/3))/9.
%F A047350 a(3k) = 7k-3, a(3k-1) = 7k-5, a(3k-2) = 7k-6. (End)
%F A047350 a(n) = 4*n - 3 - 2*floor(n/3) - 3*floor((n+1)/3). - _Ridouane Oudra_, Nov 23 2022
%p A047350 A047350:=n->(21*n-21-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047350(n), n=1..100); # _Wesley Ivan Hurt_, Jun 13 2016
%t A047350 Select[Range[0, 150], MemberQ[{1, 2, 4}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 13 2016 *)
%o A047350 (PARI) a(n)=n\3*7+[-3,1,2][n%3+1] \\ _Charles R Greathouse IV_, Jul 31 2011
%o A047350 (Magma) [n : n in [0..150] | n mod 7 in [1, 2, 4]]; // _Wesley Ivan Hurt_, Jun 13 2016
%Y A047350 Cf. A000931, A017029, A047353, A134720.
%K A047350 nonn,easy
%O A047350 1,2
%A A047350 _N. J. A. Sloane_