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%I #4 Dec 09 2017 18:58:36
%S 13,111,154,3645,2699,1394,526,613,971,39,44,60,128,149,2607,23047,
%T 21876,361554,403706,1674698,19210577
%N a(n) is the position of a(n-1) in the decimal expansion of Pi, starting with a(1)=13.
%H Dave Andersen, <a href="http://www.angio.net/pi/piquery">The Pi-Search Page</a>
%e In the decimal expansion of Pi (A000796) written as a string
%e 3141592653589793238462643383279502884197169399375105820974944592307816...,
%e the string "13" is found at position 111, the string "111" is at position 154, the string "154" at position 3645, etc.,
%e hence the sequence starting with a(1)=13 is
%e 13,111,154,3645,2699,...
%e In general, the sequence may end in a cycle, e.g. sequence s1
%e starting with a(1)=1 is
%e s1: 1,2,7,14,2,7,14,2,7,14,2 (cycle is 2,7,14),
%e Also s0, s2, s3, s4, s7, s10, s11, s14, s15, s16, s25 end with the same cycle:
%e s0: 0,33,25,90,248,480,105,50,32,16,41,3,1,2,7,14,2
%e s2: 2,7,14,2,7,14,2,
%e s3: 3,1,2,7,14,2,7,14,2
%e s4: 4,3,1, 2,7,14,2,7,14,2
%e s5: 5,5,5,5 (simplest cycle!)
%e s6: 6, 8, 12,149,2607,23047,21876,361554,403706,1674698,19210577,next term>2*10^8
%e s7: 7,14,2,7, 14, (see s1)
%e s8: 8,12,149, (see s6)
%e s9: 9,6, 8, (see s6)
%e s10: 10,50,32,16,41,3,1,2, (see s1)
%e s11: 11,95,31,1, (see s1)
%e s12: 12,149, (see s6)
%e s13: this sequence, is there cycle or not? next term>2*10^8
%e s14: 14,2, (see s1)
%e s15: 15,4,3,1, (see s1)
%e s16: 16,41,3,1, (see s1)
%e s17: 17,96,181,729,771,626,21,94,59,5,5,5,(see s5)
%e s18: 18,425,822,135,2728,11023,12721,54517,102917,183252,410024,613425,1525497,
%e 3426169,3591590,10748112, is there cycle or not? next term>2*10^8
%e s19: 19,38,18, (see s18}, is there cycle or not? next term>2*10^8
%e s20: 20,54,192,976,1808,26035,43352,93226,3603,9736,10514,54423,140517,1549413,
%e 20801035, is there cycle or not? next term>2*10^8
%e s21: 21,94,59,5,5,5,(see s5)
%e s22: 22,136,735,469,387,864,722,2140,8434,9666,4000,14637,85171,3538,5037,37934,
%e 62186,6529,37803,68887,5871,22098,172393,591481,14933,51852, 5762,7347,11749,
%e 12529,61828,268516,657761,531469,1246616,6755774,22119206,83934772,128149562,
%e is there cycle or not? next term>2*10^8
%e s23: 23,17,96,181,729,771,626,21,94,59,5,5,5, (see s17, s5)
%e s24: 24,293,572,405,596,180,3665,10143,63892,465223,522194,1637321,10980764,
%e 184160876,65620598,35543320,97248583,109914084,40782089,
%e 48875829,77976212,182755461,114041877, is there cycle or not? next term>2*10^8
%e s25: 25,90,248,480,105,50,32,16,41,3,1,2,7,14,2 (see s0, s1)
%Y Cf. A000796 = Decimal expansion of Pi, A097614 = sequence based on positions of digits in decimal digits of Pi.
%K base,nonn
%O 1,1
%A _Zak Seidov_, Jun 16 2006
%E Edited by _N. J. A. Sloane_, Dec 09 2017
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