cp's OEIS Frontend

A186041 Numbers of the form 3*k + 2, 5*k + 3, or 7*k + 4.

%I A186041 #31 Sep 08 2022 08:45:55
%S A186041 2,3,4,5,8,11,13,14,17,18,20,23,25,26,28,29,32,33,35,38,39,41,43,44,
%T A186041 46,47,48,50,53,56,58,59,60,62,63,65,67,68,71,73,74,77,78,80,81,83,86,
%U A186041 88,89,92,93,95,98,101,102,103,104,107,108,109,110,113,116,118,119,122
%N A186041 Numbers of the form 3*k + 2, 5*k + 3, or 7*k + 4.
%C A186041 n is in the sequence iff n is in A016789 or in A016885 or in A017029.
%C A186041 First differences are periodic with period length 57. Least common multiple of 3, 5, 7 is 105; number of terms <= 105 is 57.
%C A186041 Sequence is not essentially the same as A053726: a(n) = A053726(n-3) for 3 < n < 33, a(34)=62, A053726(34-3)=61.
%C A186041 Sequence is not essentially the same as A104275: a(n) = A104275(n-2) for 3 < n < 33, a(34)=62, A104275(34-3)=61.
%H A186041 G. C. Greubel, <a href="/A186041/b186041.txt">Table of n, a(n) for n = 1..1000</a>
%H A186041 <a href="/index/Rec#order_58">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
%F A186041 a(n) = a(n-57) + 105.
%F A186041 a(n) = a(n-1) + a(n-57) - a(n-58).
%F A186041 G.f.: x*(x^57 + x^56 + x^55 + x^54 + 3*x^53 + 3*x^52 + 2*x^51 + x^50 + 3*x^49 + x^48 + 2*x^47 + 3*x^46 + 2*x^45 + x^44 + 2*x^43 + x^42 + 3*x^41 + x^40 + 2*x^39 + 3*x^38 + x^37 + 2*x^36 + 2*x^35 + x^34 + 2*x^33 + x^32 + x^31 + 2*x^30 + 3*x^29 + 3*x^28 + 2*x^27 + x^26 + x^25 + 2*x^24 + x^23 + 2*x^22 + 2*x^21 + x^20 + 3*x^19 + 2*x^18 + x^17 + 3*x^16 + x^15 + 2*x^14 + x^13 + 2*x^12 + 3*x^11 + 2*x^10 + x^9 + 3*x^8 + x^7 + 2*x^6 + 3*x^5 + 3*x^4 + x^3 + x^2 + x + 2) / ((x - 1)^2*(x^2 + x + 1)*(x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1)*(x^36 - x^35 + x^33 - x^32 + x^30 - x^29 + x^27 - x^26 + x^24 - x^23 + x^21 - x^20 + x^18 - x^16 + x^15 - x^13 + x^12 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1)).
%t A186041 Take[With[{no=50},Union[Join[3Range[0,no]+2,5Range[0,no]+3,7Range[0,no]+4]]],70]  (* _Harvey P. Dale_, Feb 16 2011 *)
%o A186041 (Magma) IsA186041:=func< n | exists{ k: k in [0..n div 3] | n in [3*k+2, 5*k+3, 7*k+4] } >; [ n: n in [1..200] | IsA186041(n) ];
%Y A186041 Cf. A016789, A016885, A017029, A053726, A104275.
%K A186041 nonn,easy
%O A186041 1,1
%A A186041 _Klaus Brockhaus_, Feb 11 2011, Mar 09 2011