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A047610 Positive integers that are congruent to {1, 4, 5} mod 8.

%I A047610 #24 Sep 08 2022 08:44:57
%S A047610 1,4,5,9,12,13,17,20,21,25,28,29,33,36,37,41,44,45,49,52,53,57,60,61,
%T A047610 65,68,69,73,76,77,81,84,85,89,92,93,97,100,101,105,108,109,113,116,
%U A047610 117,121,124,125,129,132,133,137,140,141,145,148,149,153,156,157
%N A047610 Positive integers that are congruent to {1, 4, 5} mod 8.
%H A047610 Robert Israel, <a href="/A047610/b047610.txt">Table of n, a(n) for n = 1..9999</a>
%H A047610 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047610 a(n) = a(n-3) + 8, n > 3, with initial conditions a(1) = 1, a(2) = 4, a(3) = 5. - _L. Edson Jeffery_, May 04 2015
%F A047610 G.f.: x*(1+3*x)*(1+x^2)/(1-x-x^3+x^4). - _Robert Israel_, May 04 2015
%F A047610 A047610 = A016813 union A017113\{0}. - _L. Edson Jeffery_, May 06 2015
%p A047610 seq(op([8*i+1,8*i+4,8*i+5]),i=0..100); # _Robert Israel_, May 04 2015
%t A047610 a[1] := 1; a[2] := 4; a[3] := 5; a[n_] := a[n - 3] + 8; Table[a[n], {n, 10}] (* _L. Edson Jeffery_, May 04 2015 *)
%t A047610 Select[Range[0, 200], MemberQ[{1, 4, 5}, Mod[#, 8]] &] (* _Vincenzo Librandi_, May 07 2015 *)
%t A047610 LinearRecurrence[{1,0,1,-1},{1,4,5,9},60] (* _Harvey P. Dale_, Nov 21 2015 *)
%o A047610 (PARI) is(n)=n%8==1||n%8>>1==2 \\ _Charles R Greathouse IV_, May 04 2015
%o A047610 (Magma) [n : n in [0..160] | n mod 8 in [1,4,5]]; // _Vincenzo Librandi_, May 07 2015
%Y A047610 Cf. A016813, A017113.
%K A047610 nonn,easy
%O A047610 1,2
%A A047610 _N. J. A. Sloane_