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%I #45 Feb 10 2024 18:58:15
%S 2,3,4,5,8,9,10,11,14,15,16,17,20,21,22,23,26,27,28,29,32,33,34,35,38,
%T 39,40,41,44,45,46,47,50,51,52,53,56,57,58,59,62,63,64,65,68,69,70,71,
%U 74,75,76,77,80,81,82,83,86,87,88,89,92,93,94,95,98,99
%N Numbers that are congruent to {2, 3, 4, 5} (mod 6).
%C The sequence is the interleaving of A047235 with A047270. - _Guenther Schrack_, Feb 10 2019
%C Numbers k for which A276076(k) and A276086(k) are multiples of three. 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
%H Guenther Schrack, <a href="/A047247/b047247.txt">Table of n, a(n) for n = 1..10015</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>.
%F G.f.: x*(2+x+x^2+x^3+x^4) / ( (1+x)*(1+x^2)*(1-x)^2 ). - _R. J. Mathar_, Oct 08 2011
%F From _Wesley Ivan Hurt_, May 21 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = (6*n - 1 - i^(2*n) - (1-i)*i^(-n) - (1+i)*i^n)/4 where i = sqrt(-1).
%F a(2*n) = A047270(n), a(2*n-1) = A047235(n).
%F a(n) = A047227(n) + 1, a(1-n) = - A047227(n). (End)
%F From _Guenther Schrack_, Feb 10 2019: (Start)
%F a(n) = (6*n - 1 - (-1)^n -2*(-1)^(n*(n+1)/2))/4.
%F a(n) = a(n-4) + 6, a(1)=2, a(2)=3, a(3)=4, a(4)=5, for n > 4.
%F a(n) = A047227(n) + 1. a(n) = A047246(n) + 2. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/12 - 2*log(2)/3 + log(3)/4. - _Amiram Eldar_, Dec 17 2021
%p A047247:=n->(6*n-1-I^(2*n)-(1-I)*I^(-n)-(1+I)*I^n)/4: seq(A047247(n), n=1..100); # _Wesley Ivan Hurt_, May 21 2016
%t Table[(6n-1-I^(2n)-(1-I)*I^(-n)-(1+I)*I^n)/4, {n, 80}] (* _Wesley Ivan Hurt_, May 21 2016 *)
%o (Magma) [n : n in [0..100] | n mod 6 in [2, 3, 4, 5]]; // _Wesley Ivan Hurt_, May 21 2016
%o (PARI) my(x='x+O('x^70)); Vec(x*(2+x+x^2+x^3+x^4)/((1-x)*(1-x^4))) \\ _G. C. Greubel_, Feb 16 2019
%o (Sage) a=(x*(2+x+x^2+x^3+x^4)/((1-x)*(1-x^4))).series(x, 72).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, Feb 16 2019
%Y Cf. A047227, A047235, A047246, A047270, A047257.
%Y Cf. A007623, A049345, A276076, A276086.
%Y Complement: A047225.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _Wesley Ivan Hurt_, May 21 2016
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