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A119744 a(n) is the position of a(n-1) in the decimal expansion of Pi, a(1)=13. 0
13, 111, 154, 3645, 2699, 1394, 526, 613, 971, 39, 44, 60, 128, 149, 2607, 23047, 21876, 361554, 403706, 1674698, 19210577 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A000796 Decimal expansion of Pi, A097614 Recurrence sequence based on positions of digits in decimal places of Pi.

LINKS

Table of n, a(n) for n=1..21.

Dave Andersen, The Pi-Search Page

EXAMPLE

In the decimal expansion of P A000796 written down as string:

3141592653589793238462643383279502884197169399375105820974944592307816

the string "13" is found at position 111, the string "111" is at position 154, the string "154" at position 3645, etc.,

hence the sequence starting with a(1)=13 is

13,111,154,3645,2699,...

In general, the sequence may end in cycle, e.g. sequence s1

starting with a(1)=1 is

s1: 1,2,7,14,2,7,14,2,7,14,2 (cycle 2,7,14,2),

Also s0, s2, s3, s4, s7, s10, s11, s14, s15, s16, s25 end with the same cycle:

s0: 0,33,25,90,248,480,105,50,32,16,41,3,1,2,7,14,2

s2: 2,7,14,2,7,14,2,

s3: 3,1,2,7,14,2,7,14,2

s4: 4,3,1, 2,7,14,2,7,14,2

s5: 5,5,5,5 (simplest cycle!)

s6: 6, 8, 12,149,2607,23047,21876,361554,403706,1674698,19210577,next term>2*10^8

s7: 7,14,2,7, 14, (see s1)

s8: 8,12,149, (see s6)

s9: 9,6, 8, (see s6)

s10: 10,50,32,16,41,3,1,2, (see s1)

s11: 11,95,31,1, (see s1)

s12: 12,149, (see s6)

s13: this sequence, is there cycle or not? next term>2*10^8

s14: 14,2, (see s1)

s15: 15,4,3,1, (see s1)

s16: 16,41,3,1, (see s1)

s17: 17,96,181,729,771,626,21,94,59,5,5,5,(see s5)

s18: 18,425,822,135,2728,11023,12721,54517,102917,183252,410024,613425,1525497,

3426169,3591590,10748112, is there cycle or not? next term>2*10^8

s19: 19,38,18, (see s18}, is there cycle or not? next term>2*10^8

s20: 20,54,192,976,1808,26035,43352,93226,3603,9736,10514,54423,140517,1549413,

20801035, is there cycle or not? next term>2*10^8

s21: 21,94,59,5,5,5,(see s5)

s22: 22,136,735,469,387,864,722,2140,8434,9666,4000,14637,85171,3538,5037,37934,

62186,6529,37803,68887,5871,22098,172393,591481,14933,51852, 5762,7347,11749,

12529,61828,268516,657761,531469,1246616,6755774,22119206,83934772,128149562,

is there cycle or not? next term>2*10^8

s23: 23,17,96,181,729,771,626,21,94,59,5,5,5, (see s17, s5)

s24: 24,293,572,405,596,180,3665,10143,63892,465223,522194,1637321,10980764,

184160876,65620598,35543320,97248583,109914084,40782089,

48875829,77976212,182755461,114041877, is there cycle or not? next term>2*10^8

s25: 25,90,248,480,105,50,32,16,41,3,1,2,7,14,2 (see s0, s1)

CROSSREFS

Cf. A000796, A097614.

Sequence in context: A005769 A042941 A021344 * A099111 A199642 A087609

Adjacent sequences:  A119741 A119742 A119743 * A119745 A119746 A119747

KEYWORD

base,nonn,uned

AUTHOR

Zak Seidov, Jun 16 2006

STATUS

approved

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Last modified November 23 19:50 EST 2014. Contains 249865 sequences.