A186041 - OEIS

%I #31 Sep 08 2022 08:45:55

%S 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 46,47,48,50,53,56,58,59,60,62,63,65,67,68,71,73,74,77,78,80,81,83,86,

%U 88,89,92,93,95,98,101,102,103,104,107,108,109,110,113,116,118,119,122

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

%C n is in the sequence iff n is in A016789 or in A016885 or in A017029.

%C First differences are periodic with period length 57. Least common multiple of 3, 5, 7 is 105; number of terms <= 105 is 57.

%C 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 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 G. C. Greubel, <a href="/A186041/b186041.txt">Table of n, a(n) for n = 1..1000</a>

%H <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 a(n) = a(n-57) + 105.

%F a(n) = a(n-1) + a(n-57) - a(n-58).

%F 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 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 (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 Cf. A016789, A016885, A017029, A053726, A104275.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Feb 11 2011, Mar 09 2011