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Search: id:A137506
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| A137506 |
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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... |
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| 141, 59, 265, 35, 389, 11, 513, 13, 637, 11, 761, 13, 885, 11, 1009, 13, 1133, 11, 1257, 13, 1381, 11, 1505, 13, 1629, 11, 1753, 13, 1877, 11, 2001, 13, 2125, 11, 2249, 13, 2373, 11, 2497, 13, 2621, 11, 2745, 13, 2869, 11, 2993, 13, 3117, 11, 3241, 13, 3365
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OFFSET
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1,1
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COMMENT
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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
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)).
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...
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FORMULA
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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)
a(n) = a(n-2) + a(n-4) - a(n-6) a(n) = 81 - 37*(-1)^n*n + 2*(-1)^n + 25*n
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PROGRAM
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(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; }
(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
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CROSSREFS
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Sequence in context: A091755 A058939 A165600 this_sequence A036192 A045935 A144799
Adjacent sequences: A137503 A137504 A137505 this_sequence A137507 A137508 A137509
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KEYWORD
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nonn,base
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AUTHOR
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Alexander R. Povolotsky (pevnev(AT)juno.com), Apr 23 2008
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EXTENSIONS
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Edited & extended by M. F. Hasler (www.univ-ag.fr/~mhasler), May 01 2008
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