A014777 -id:A014777 - cp's OEIS frontend

A280532 a(1) = a(2) = 1, a(n) = A014777(a(n-1) + a(n-2)), n >= 3.

1, 1, 6, 13, 37, 31, 605, 1411, 7174, 15567, 608953, 78903, 334535, 611552, 105928, 2557047, 2979162, 3263358, 6242520, 7825254, 37404834, 267494881, 639174488

Offset: 1

Anders Hellström, Jan 13 2017

Dave Andersen, Probability of Finding Strings In Pi
Anders Hellström, Sage program
James Taylor, Irrational Numbers Search Engine (Search 2*10^9 decimal digits of Pi)

Cf. A014777, A032445, A038100, A176341, A232013.

Module[{a = {1, 1}, s = First@ RealDigits[N[Pi, 10^7]]}, Do[AppendTo[a, -1 + SequencePosition[s, IntegerDigits[ a[[n - 1]] + a[[n - 2]] ]][[1, 1]]], {n, 3, 20}]; a] (* Michael De Vlieger, Jan 14 2017 *)

A134203 Duplicate of A014777.

Original entry on oeis.org

32, 1, 6, 9, 2, 4, 7, 13, 11, 5, 49, 94, 148, 110, 1, 3, 40, 95, 424, 37, 53, 93, 135, 16, 292, 89, 6, 28, 33, 186, 64, 137

Offset: 0

dead

A097614 In the decimal expansion of Pi, the string "0" is found at position 32 counting from the first digit after the decimal point. The string "32" is found at position 15, the string "15" at position 3, the string "3" at position 9, etc.

Original entry on oeis.org

0, 32, 15, 3, 9, 5, 4, 2, 6, 7, 13, 110, 174, 155, 314, 2120, 5360, 24671, 119546, 193002, 240820, 274454, 153700, 1397287, 17916598, 26245242, 8880928, 7320921, 14726415, 42969065, 35308126, 14978764, 68756682, 300921774

Offset: 0

Eric Angelini, Aug 30 2004

Dave Andersen, The Pi-Search Page.
Anders Hellström, Sage program

Cf. A014777.

Function[c, NestList[SequencePosition[c, IntegerDigits@ #][[1, 1]] &, 0, 23]]@ Rest@ First@ RealDigits[N[Pi, 10^7]] (* Michael De Vlieger, Jan 23 2017, Version 10.1 *)

M97614=[]; A097614(n)={while(n > #M97614, M97614=concat(M97614, A014777(A097614(#M97614)))); if(n, M97614[n],0)} \\ M. F. Hasler, Jun 21 2022

def A097614(n):
    while n >= len(A097614.list):
        A097614.list.append(A014777(A097614.list[-1]))
    return A097614.list[n]
A097614.list = [0] # M. F. Hasler, Jun 21 2022

a(0) = 0, a(1) = A014777(0) = 32, a(n) = A014777(a(n-1)), for n>1. - Anders Hellström, Jan 21 2017

a(33) from Michael S. Branicky, Dec 05 2024

A176341 a(n) = the location of the first appearance of the decimal expansion of n in the decimal expansion of Pi.

Original entry on oeis.org

32, 1, 6, 0, 2, 4, 7, 13, 11, 5, 49, 94, 148, 110, 1, 3, 40, 95, 424, 37, 53, 93, 135, 16, 292, 89, 6, 28, 33, 186, 64, 0, 15, 24, 86, 9, 285, 46, 17, 43, 70, 2, 92, 23, 59, 60, 19, 119, 87, 57, 31, 48, 172, 8, 191, 130, 210, 404, 10, 4, 127, 219, 20, 312, 22, 7, 117, 98, 605, 41

Offset: 0

Daniel E. Loeb, Apr 15 2010

It is unknown whether Pi is a normal number. If it is (at least in base 10) then this sequence is well defined.

The numbers a(n) refer to the position of the initial digit of n in the decimal expansion of Pi, where "3" is at position a(3)=0, "1" is at position a(1)=1, etc. This is also the numbering scheme used on the "Pi search page" cited among the LINKS. See A232013 for a sequence based on iterations of this one. See A032445 for a variant of the present sequence, where numbering starts at one. - M. F. Hasler, Nov 16 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Dave Andersen, Search within first 200,000,000 digits of pi
Michael D. Huberty, Ko Hayashi & Chia Vang, First 100,000 digits of pi
Simon Plouffe, First 50,000,000 digits of pi

Cf. A000796, A011545, A014777, A032445, A232013.

p=ToString[FromDigits[RealDigits[N[Pi, 10^4]][[1]]]]; Do[Print[StringPosition[p, ToString[n]][[1]][[1]] - 1], {n, 0, 100}] (* Vincenzo Librandi, Apr 17 2017 *)
With[{pid=RealDigits[Pi,10,800][[1]]},Flatten[Table[ SequencePosition[ pid,IntegerDigits[n],1],{n,0,70}],1]][[All,1]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 27 2019 *)

A176341(n)=my(L=#Str(n));n=Mod(n,10^L);for(k=L-1,9e9,Pi\.1^k-n||return(k+1-L)) \\ Make sure to use sufficient realprecision, e.g. via \p999. - M. F. Hasler, Nov 16 2013

pi = "314159265358979323846264338327950288419716939937510582097494459230..."
[ pi.find(str(i)) for i in range(10000) ]

a(n) = A032445(n)-1. - M. F. Hasler, Nov 16 2013

a(n) = 0 if n is in A011545, otherwise a(n) = A014777(n). - Pontus von Brömssen, Aug 31 2024

A098266 a(1)=0; for i>=1, a(i+1)=position of first occurrence of a(i) in decimal expansion of e.

Original entry on oeis.org

0, 13, 27, 62, 32, 110, 3188, 12078, 141356, 2085932, 3497082, 4910326, 929922, 1189814, 4196683, 1301478, 19560712, 6894489, 41960008

Offset: 0

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 01 2004

Recurrence sequence based on positions of digits in decimal places of e.

			So for example, a(2)=13 because 13th digit of e after decimal point is 0.
a(3)=27 because 27th decimal digit of e is 13, a(4)=62 because 62nd to 63rd decimal digits of e form "13" and so on.

Cf. A078197 for the first occurrence of integers in decimal digits of e; A097614 for the analogous recurrence sequence for Pi, also A014777 for positions of integers in decimal digits of Pi.

More terms from Ben Ross (bmr180(AT)psu.edu), Feb 01 2006

A134251 Positions of 1 after decimal point in decimal expansion of 1/Pi.

Original entry on oeis.org

2, 10, 18, 41, 45, 50, 64, 65, 82, 97, 99, 101, 103, 113, 116, 133, 147, 170, 172, 175, 178, 191, 251, 252, 255, 265, 275, 285, 295, 297, 304, 329, 333, 340, 346, 350, 379, 385, 399, 410, 418, 432, 433, 443, 459, 473, 485, 493, 494, 509, 515, 519, 553, 558

Offset: 1

Artur Jasinski, Oct 16 2007

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A037000, A014777, A134251, A134252, A134253, A134254, A134255, A134256, A134257, A134258, A134259, A134260.

Flatten @ Position[RealDigits[1/Pi, 10, 500][[1]], 1] (* Amiram Eldar, Mar 21 2020 *)

A134252 Positions of 2 after decimal point in decimal expansion of 1/Pi.

Original entry on oeis.org

26, 32, 35, 43, 51, 73, 85, 86, 93, 102, 125, 129, 130, 131, 146, 183, 204, 212, 218, 229, 233, 241, 242, 260, 276, 277, 284, 309, 331, 332, 351, 357, 359, 389, 393, 403, 409, 425, 438, 447, 448, 458, 479, 482, 505, 534, 540, 550, 562, 564, 577, 581, 612, 620

Offset: 1

Artur Jasinski, Oct 16 2007

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Cf. A037000, A014777, A134251, A134253, A134254, A134255, A134256, A134257, A134258, A134259, A134260.

Flatten[Position[RealDigits[1/Pi,10,700][[1]],2]] (* Harvey P. Dale, Apr 22 2014 *)

A134253 Positions of 3 after decimal point in decimal expansion of 1/Pi.

Original entry on oeis.org

1, 4, 12, 20, 58, 59, 69, 78, 92, 111, 120, 126, 136, 143, 150, 151, 164, 165, 186, 193, 197, 206, 211, 213, 214, 225, 234, 247, 254, 261, 267, 271, 288, 319, 342, 352, 353, 354, 364, 370, 373, 378, 384, 386, 387, 416, 421, 436, 439, 449, 452, 455, 457, 462

Offset: 1

Artur Jasinski, Oct 16 2007

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A037000, A014777, A134251, A134252, A134254, A134255, A134256, A134257, A134258, A134259, A134260.

Flatten[Position[RealDigits[1/Pi,10,500][[1]],3]] (* Harvey P. Dale, Sep 18 2013 *)

A134254 Positions of 4 after decimal point in decimal expansion of 1/Pi.

Original entry on oeis.org

29, 36, 46, 55, 60, 76, 104, 109, 144, 148, 157, 160, 168, 176, 181, 196, 198, 205, 207, 219, 223, 226, 227, 237, 244, 245, 253, 272, 278, 301, 302, 316, 320, 321, 325, 338, 347, 372, 380, 391, 401, 426, 437, 456, 475, 498, 513, 523, 524, 527, 537, 542, 547

Offset: 1

Artur Jasinski, Oct 16 2007

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A037000, A014777, A134251, A134252, A134253, A134255, A134256, A134257, A134258, A134259, A134260.

Flatten[Position[RealDigits[1/\[Pi] ,10,1000][[1]],4]]  (* Harvey P. Dale, Mar 20 2011 *)

A134255 Positions of 5 after decimal point in decimal expansion of 1/Pi.

Original entry on oeis.org

19, 25, 30, 57, 70, 72, 77, 90, 91, 94, 105, 108, 110, 112, 114, 123, 134, 138, 140, 141, 158, 173, 174, 179, 180, 188, 192, 201, 210, 230, 246, 250, 270, 291, 299, 324, 343, 360, 375, 382, 429, 431, 440, 450, 454, 465, 484, 490, 512, 517, 518, 529, 530, 531

Offset: 1

Artur Jasinski, Oct 16 2007

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A037000, A014777, A134251, A134252, A134253, A134254, A134256, A134257, A134258, A134259, A134260.

Flatten @ Position[RealDigits[1/Pi, 10, 500][[1]], 5] (* Amiram Eldar, Mar 21 2020 *)

cp's OEIS Frontend

A280532 a(1) = a(2) = 1, a(n) = A014777(a(n-1) + a(n-2)), n >= 3.

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A134203 Duplicate of A014777.

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A097614 In the decimal expansion of Pi, the string "0" is found at position 32 counting from the first digit after the decimal point. The string "32" is found at position 15, the string "15" at position 3, the string "3" at position 9, etc.

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A176341 a(n) = the location of the first appearance of the decimal expansion of n in the decimal expansion of Pi.

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A098266 a(1)=0; for i>=1, a(i+1)=position of first occurrence of a(i) in decimal expansion of e.

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A134251 Positions of 1 after decimal point in decimal expansion of 1/Pi.

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A134252 Positions of 2 after decimal point in decimal expansion of 1/Pi.

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A134253 Positions of 3 after decimal point in decimal expansion of 1/Pi.

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A134254 Positions of 4 after decimal point in decimal expansion of 1/Pi.

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A134255 Positions of 5 after decimal point in decimal expansion of 1/Pi.

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