Search: id:A035106
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%I A035106
%S A035106 1,2,3,6,8,12,15,20,24,30,35,42,48,56,63,72,80,90,99,110,120,132,143,
%T A035106 156,168,182,195,210,224,240,255,272,288,306,323,342,360,380,399,420,
%U A035106 440,462,483,506,528,552,575,600,624,650,675,702,728,756,783,812,840
%N A035106 Largest integer m such that every permutation (p_1, ..., p_n) of (1, 
               ..., n) satisfies p_i * p_{i+1}) >= m for some i, 1 <= i <= n-1.
%C A035106 Equivalently, smallest integer m such that there exists a permutation 
               (p_1, ..., p_n) of (1, ..., n) satisfying p_i * p_{i+1} <= m for 
               every i, 1 <= i <= n-1.
%C A035106 Nonsquare positive integers m such that [sqrt(m)] divides m. Numbers 
               of the form k*(k+1) or k*(k+2). - Max Alekseyev (maxale(AT)gmail.com), 
               Nov 27 2006
%F A035106 Theorem: a(n)=n*(n+2)/4 if n is even and (n-1)*(n+3)/4 if n is odd, n>
               1. - Jud McCranie (j.mccranie(AT)comcast.net), Oct 25 2001
%F A035106 a(n) = a(n-1)+a(n-2)-a(n-3)+1 = A002620(n+2)+A004526(n+2) - Henry Bottomley 
               (se16(AT)btinternet.com), Mar 08 2000
%F A035106 a(n+2) = (2*n^2+12*n+3*(-1)^n+13)/8, i.e. a(n+2) = (n+2)*(n+4)/4 if n 
               is even and (n+1)*(n+5)/4 if n is odd. G.f.: (2-x)/(1-2*x+2*x^3-x^4). 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 23 2001
%F A035106 {a[n] == a[n - 2] + (n - 1), a[1] == 0, a[2] == 0}; (-4 - 3*(-1)^n - 
               (-1)^(2*n) + 2*n - 2*(-1)^(2*n)*n + 2*n^2)/8 - Cecilia Rossiter (cecilia(AT)noticingnumbers.net), 
               Dec 14 2004
%e A035106 n=5: we must arrange the numbers 1..5 so that the max of the products 
               of pairs of adjacent terms is minimized. The answer is 51324, with 
               max product = 8, so a(5) = 8.
%Y A035106 Cf. A064764, A064796, A064797, A064817, A004652, A035104, A035107.
%Y A035106 First differences give (essentially) A028242.
%Y A035106 Bisections: A002378 (pronic numbers) and A005563.
%Y A035106 Cf. A002378, A006446.
%Y A035106 Sequence in context: A098393 A103567 A131723 this_sequence A122378 A111242 
               A133582
%Y A035106 Adjacent sequences: A035103 A035104 A035105 this_sequence A035107 A035108 
               A035109
%K A035106 nonn,nice
%O A035106 1,2
%A A035106 N. J. A. Sloane (njas(AT)research.att.com), revised Oct 30, 2001

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