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A047372 Numbers that are congruent to {1, 2, 3, 5} mod 7.

%I A047372 #25 Jun 29 2025 21:36:22
%S A047372 1,2,3,5,8,9,10,12,15,16,17,19,22,23,24,26,29,30,31,33,36,37,38,40,43,
%T A047372 44,45,47,50,51,52,54,57,58,59,61,64,65,66,68,71,72,73,75,78,79,80,82,
%U A047372 85,86,87,89,92,93,94,96,99,100,101,103,106,107,108,110
%N A047372 Numbers that are congruent to {1, 2, 3, 5} mod 7.
%H A047372 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A047372 From _Bruno Berselli_, Dec 01 2010: (Start)
%F A047372 G.f.: x*(1+x+x^2+2*x^3+2*x^4) / ((1-x)^2*(1+x+x^2+x^3)).
%F A047372 a(n) = (14*n+(3*i-1)*(-i)^n-(3*i+1)*i^n-(-1)^n-13)/8, i=sqrt(-1). (End)
%F A047372 From _Wesley Ivan Hurt_, Jun 04 2016: (Start)
%F A047372 a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F A047372 a(2k) = A047385(k), a(2k-1) = A047356(k). (End)
%F A047372 E.g.f.: (8 + 3*sin(x) - cos(x) + (7*x - 6)*sinh(x) + 7*(x - 1)*cosh(x))/4. - _Ilya Gutkovskiy_, Jun 04 2016
%p A047372 A047372:=n->(14*n+(3*I-1)*(-I)^n-(3*I+1)*I^n-(-1)^n-13)/8: seq(A047372(n), n=1..100); # _Wesley Ivan Hurt_, Jun 04 2016
%t A047372 Flatten[7Range[0,12]+n/.n->{1,2,3,5}] (* _Harvey P. Dale_, Dec 13 2010 *)
%o A047372 (Magma) [n : n in [0..150] | n mod 7 in [1, 2, 3, 5]]; // _Wesley Ivan Hurt_, Jun 04 2016
%Y A047372 Cf. A047356, A047385.
%K A047372 nonn,easy
%O A047372 1,2
%A A047372 _N. J. A. Sloane_