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A047425 Numbers that are congruent to {3, 4, 5, 6} mod 8.

%I A047425 #31 Sep 08 2022 08:44:57
%S A047425 3,4,5,6,11,12,13,14,19,20,21,22,27,28,29,30,35,36,37,38,43,44,45,46,
%T A047425 51,52,53,54,59,60,61,62,67,68,69,70,75,76,77,78,83,84,85,86,91,92,93,
%U A047425 94,99,100,101,102,107,108,109,110,115,116,117,118,123,124
%N A047425 Numbers that are congruent to {3, 4, 5, 6} mod 8.
%C A047425 Complement of numbers congruent to {0, 1, 2, 7} mod 8. - _Jaroslav Krizek_, Dec 19 2009
%C A047425 In general, sequences congruent to {a, a + i, a + 2i, ..., a + pi} mod k  and a + p*i < k have a general form of (k - i*p)*floor(n/p) + i*n + a, from offset 0. - _Gary Detlefs_, Oct 20 2013
%H A047425 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047425 G.f.: x*(3+x+x^2+x^3+2*x^4) / ( (1+x)*(x^2+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F A047425 a(n) = 8*floor((n-1)/4) + ((n-1) mod 4) + 3.
%F A047425 a(n) = OR(n-1, 1) + OR(n-1, 2). - _Gary Detlefs_, Oct 20 2013
%F A047425 From _Wesley Ivan Hurt_, May 31 2016: (Start)
%F A047425 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047425 a(n) = (4*n-1-i^(2*n)-(1-i)*i^(-n)-(1+i)*i^n)/2 where i=sqrt(-1).
%F A047425 a(2k) = A047406(k), a(2k-1) = A047621(k). (End)
%F A047425 E.g.f.: 2 + sin(x) - cos(x) + 2*x*sinh(x) + (2*x - 1)*cosh(x). - _Ilya Gutkovskiy_, May 31 2016
%F A047425 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/16 + (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2-sqrt(2))/4. - _Amiram Eldar_, Dec 26 2021
%p A047425 A047425:=n->8*floor((n-1)/4)+((n-1) mod 4)+3: seq(A047425(n), n=1..100); # _Wesley Ivan Hurt_, May 31 2016
%t A047425 Flatten[# + {3, 4, 5, 6} &/@(8*Range[0, 15])] (* _Harvey P. Dale_, Jun 26 2011 *)
%o A047425 (Magma) [n : n in [0..150] | n mod 8 in [3, 4, 5, 6]]; // _Wesley Ivan Hurt_, May 31 2016
%Y A047425 Cf. A047406, A047621.
%K A047425 nonn,easy
%O A047425 1,1
%A A047425 _N. J. A. Sloane_