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a(n) = floor(3*n^2/4) - 1.
1

%I #19 May 08 2022 16:33:18

%S 2,5,11,17,26,35,47,59,74,89,107,125,146,167,191,215,242,269,299,329,

%T 362,395,431,467,506,545,587,629,674,719,767,815,866,917,971,1025,

%U 1082,1139,1199,1259,1322,1385,1451,1517,1586,1655,1727,1799,1874,1949,2027

%N a(n) = floor(3*n^2/4) - 1.

%C This sequence has a relatively high density of primes given its simple formula and high values: 38 in the first 100. The composites in the first 157 elements are mainly p1*p2 or p1*p2^2 or p^1^3, with the rest having three distinct primes. The first composite of four distinct primes is at n = 158, a(n)= 18722 = 2*11*23*37.

%H Harvey P. Dale, <a href="/A228344/b228344.txt">Table of n, a(n) for n = 2..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F Floor(3n^2/4) - 1 = A007590(n) + A002620(n) - 1 = 3*A002620 - 1.

%F a(n) = (-11+3*(-1)^n+6*n^2)/8. a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). G.f.: x^2*(x-2)*(x^2+x+1) / ((x-1)^3*(x+1)). - _Colin Barker_, Aug 27 2013

%e a(14) = floor(3*14^2/4)-1 = 146.

%t Table[Floor[3*n^2/4] - 1, {n, 2, 100}] (* _T. D. Noe_, Aug 23 2013 *)

%t LinearRecurrence[{2,0,-2,1},{2,5,11,17},60] (* _Harvey P. Dale_, May 08 2022 *)

%Y Cf. A002620, A007590.

%K nonn,easy

%O 2,1

%A _Richard R. Forberg_, Aug 20 2013

%E a(14) corrected by _Colin Barker_, Aug 27 2013