Search: id:A137506
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%I A137506
%S A137506 141,59,265,35,389,11,513,13,637,11,761,13,885,11,1009,13,1133,11,1257,
%T A137506 13,1381,11,1505,13,1629,11,1753,13,1877,11,2001,13,2125,11,2249,13,
%U A137506 2373,11,2497,13,2621,11,2745,13,2869,11,2993,13,3117,11,3241,13,3365
%N A137506 a(2n+1)=141+124n, a(2n+2)=|a(2n)-24| with a(2)=59, thus a(4,6,8,...)=35,
               11,13,11,13...
%C A137506 The definition of this sequence is inspired by the first 3+2+3+2 decimals 
               of Pi, which have the property that 141+59=200, 265+35=300. The following 
               3+2 digits don't share such a property, but are followed by digits 
               238,462 with sum 700... - M. F. Hasler, May 01 2008
%C A137506 Using the given formula for a(n) we could construct d(n)= sum(k=1,n,(81 
               - (37*(-1)^k)*k + 2*(-1)^k + 25*k)/10^(1/4-1/4*(-1)^k+5/2*k)).
%C A137506 E.g. sum(k=1,6,(81 + (37*(-1)^(k+1) + 25)*k + 2*(-1)^k)/10^(1/4*(1 + 
               (-1)^(k+1) + 10*k))) = 0.141592653538911 and sum(k=1..oo,(81 - (37*(-1)^k)*k 
               + 2*(-1)^k + 25*k)/10^(1/4-1/4*(-1)^k+5/2*k)) = 0.1415926535389115128763663759...
%F A137506 G.f.: (22*x^9 + 26*x^7 - 83*x^5 - 17*x^4 - 24*x^3 + 124*x^2 + 59*x +141) 
               /(x^6 -x^4 - x^2 + 1)
%F A137506 a(n) = a(n-2) + a(n-4) - a(n-6) a(n) = 81 - 37*(-1)^n*n + 2*(-1)^n + 
               25*n
%o A137506 (PARI) a(n) = {local(a = vector(n)); a[1]=141; a[2]=59; for(m=3,n, if((Mod(m,
               2))==0, a[m]=abs(a[m-3]+a[m-2]+100-a[m-1])); if((Mod(m,2))!=0, a[m]=a[m-2]+124; 
               ); ); a; }
%o A137506 (PARI) A137506(n)=if( n%2, 141+n\2*124, if( n<6, [59,35][n\2], [11,13][1+!(n%4)])) 
               \\ - M. F. Hasler, May 01 2008
%Y A137506 Sequence in context: A091755 A058939 A165600 this_sequence A036192 A045935 
               A144799
%Y A137506 Adjacent sequences: A137503 A137504 A137505 this_sequence A137507 A137508 
               A137509
%K A137506 nonn,base
%O A137506 1,1
%A A137506 Alexander R. Povolotsky (pevnev(AT)juno.com), Apr 23 2008
%E A137506 Edited & extended by M. F. Hasler (www.univ-ag.fr/~mhasler), May 01 2008

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