A014777 -id:A014777 - cp's OEIS frontend

A128050 Position of start of first occurrence of prime(n) after the decimal point in expansion of golden ratio phi.

19, 5, 22, 10, 34, 55, 35, 188, 131, 174, 137, 98, 90, 27, 102, 111, 166, 1, 150, 217, 479, 44, 25, 13, 81, 458, 1242, 744, 563, 96, 1602, 186, 97, 995, 259, 939, 1999, 1204, 641, 1191, 43, 833, 1682, 2833, 2708, 188, 647, 130, 62, 734, 2337, 1106, 307, 1156, 2532

Offset: 1

Gregory Allen, Feb 13 2007

			Golden ratio phi = 1.6180339887498948482045868343656381177... (see A001622).
First occurrence of prime(1) = 2 is at the 19th digit after the decimal point, hence a(1) = 19.
First occurrence of prime(5) = 11 starts at the 34th digit after the decimal point, hence a(5) = 34.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A001622, A037024, A014777.

k:=3000; R := RealField(k); [ Position(IntegerToString(Round(10^k*(-1 + (Sqrt(elt)+1) / elt))), IntegerToString(NthPrime(n))) : n in [1..55] ]; /* Klaus Brockhaus, Feb 15 2007 */

Module[{p = Rest[First[RealDigits[GoldenRatio, 10, 10^4]]], n = 0, a}, Reap[While[(a = SequencePosition[p, IntegerDigits[Prime[++n]], 1]) != {}, Sow[a[[1, 1]]]]][[2, 1]]] (* Paolo Xausa, Aug 01 2024 *)

Edited, corrected and extended by Klaus Brockhaus, Feb 15 2007

A133268 a(n) = positions of 0's after decimal point in decimal expansion of 1/Pi.

Original entry on oeis.org

5, 15, 31, 37, 48, 79, 81, 84, 89, 95, 118, 137, 189, 222, 232, 240, 258, 264, 269, 279, 298, 314, 315, 362, 371, 394, 435, 451, 460, 463, 466, 472, 480, 497, 507, 510, 520, 521, 525, 541, 565, 569, 571, 596, 600, 606, 609, 610, 636, 670, 702, 703, 706, 707

Offset: 1

Artur Jasinski, Oct 16 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A037008, A049541, A014777.

Flatten[Position[RealDigits[1/Pi,10,1000][[1]],0]] (* Harvey P. Dale, May 16 2012 *)

A134210 Positions of 10 after the decimal point in the decimal expansion of Pi.

Original entry on oeis.org

49, 163, 175, 206, 269, 442, 681, 780, 852, 854, 1011, 1219, 1223, 1270, 1318, 1487, 1816, 1892, 2162, 2238, 2514, 2534, 2563, 2721, 2749, 2780, 2810, 2874, 2880, 2955, 3170, 3201, 3208, 3241, 3254, 3405, 3457, 3480, 3486, 3494, 3845, 3848, 3939, 3964, 3966

Offset: 1

Artur Jasinski, Oct 14 2007

Harvey P. Dale, Table of n, a(n) for n = 1..2000

Cf. A000796 (Pi).

Cf. A037008, A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037007, A014777.

SequencePosition[RealDigits[Pi,10,10000][[1]],{1,0}][[All,1]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 20 2016 *)

More terms from Harvey P. Dale, Nov 20 2016

A256521 Table T(n, k) of positions p[i] where number n occurs after the decimal point in the decimal expansion of Pi, read by antidiagonals.

Original entry on oeis.org

32, 50, 1, 54, 3, 6, 65, 37, 16, 9, 71, 40, 21, 15, 2, 77, 49, 28, 17, 19, 4, 85, 68, 33, 24, 23, 8, 7, 97, 94, 53, 25, 36, 10, 20, 13, 106, 95, 63, 27, 57, 31, 22, 29, 11, 116, 103, 73, 43, 59, 48, 41, 39, 18, 5, 121, 110, 76, 46, 60, 51, 69, 47, 26, 12, 49, 128, 138, 83, 64, 70, 61, 72, 56, 34, 14, 163, 94

Offset: 0

Felix Fröhlich, Apr 01 2015

Table T(n, k) starts:
n =  0: 32,  50,  54,  65,  71,  77,  85,  97, 106, 116, ...
n =  1:  1,   3,  37,  40,  49,  68,  94,  95, 103, 110, ...
n =  2:  6,  16,  21,  28,  33,  53,  63,  73,  76,  83, ...
n =  3:  9,  15,  17,  24,  25,  27,  43,  46,  64,  86, ...
n =  4:  2,  19,  23,  36,  57,  59,  60,  70,  87,  92, ...
n =  5:  4,   8,  10,  31,  48,  51,  61,  90, 109, 130, ...
n =  6:  7,  20,  22,  41,  69,  72,  75,  82,  98, 108, ...
n =  7: 13,  29,  39,  47,  56,  66,  96,  99, 120, 139, ...
n =  8: 11,  18,  26,  34,  35,  52,  67,  74,  78,  81, ...
n =  9:  5,  12,  14,  30,  38,  42,  44,  45,  55,  58, ...
n = 10: 49, 163, 175, 206, 269, 442, 681, 780, 852, 854, ...
...

			T(6, 4) = 41, since the fourth occurrence of 6 in the decimal expansion of Pi is at position 41.

Robert G. Wilson v, Table of n, a(n) for n = 0..1000
D. G. Andersen, The Pi-Search Page

Cf. A000796 (Pi), A014777 (first column).
Cf. A037008, A037000, A037001, A037002, A037003 (0th to 4th row).
Cf. A037004, A037005, A036974, A037006, A037007 (5th to 9th row).

spi = StringDrop[ ToString[ N[ Pi, 1000]], 2]; t[n_, k_] := StringPosition[ spi, ToString[n], k][[-1, 1]]; Table[ t[n - k, k], {n, 0, 12}, {k, n, 1, -1}] // Flatten (* Robert G. Wilson v, Apr 07 2015 *)

More terms from Robert G. Wilson v, Apr 07 2015

A332929 Position where the binary expansion of n occurs for the first time in the binary expansion of Pi.

Original entry on oeis.org

3, 1, 2, 1, 2, 18, 1, 13, 8, 2, 21, 18, 1, 17, 16, 13, 8, 27, 2, 62, 25, 21, 18, 93, 49, 1, 20, 17, 95, 16, 15, 13, 97, 8, 27, 45, 2, 128, 62, 146, 25, 60, 21, 395, 229, 18, 93, 209, 49, 65, 1, 78, 42, 20, 17, 105, 95, 116, 186, 16, 175, 15, 14, 13, 97, 110

Offset: 0

Thomas König, Mar 02 2020

			In binary, Pi = 11.00100100.... The bitstring 10 (for 2) occurs at position 2, so a(2) = 2.

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A004601, A014777, A178707.

Cf. A032445 (for decimal expansion rather than binary).

p = RealDigits[Pi,2,500][[1]]; L = {}; Do[t = SequencePosition[p, IntegerDigits[n, 2], 1]; If[t == {}, Break[], AppendTo[L, t[[1, 1]]]], {n, 0, 65}]; L (* Giovanni Resta, Mar 16 2020 *)
Module[{nn=500,bp},bp=RealDigits[Pi,2,nn][[1]];Table[ SequencePosition[ bp,IntegerDigits[n,2],1][[All,1]],{n,0,70}]]//Flatten (* Harvey P. Dale, Sep 18 2021 *)

#! /usr/bin/perl
# Feed b004601.txt to this to get the binary digits of Pi.
while (<>) {
    chomp;
    (undef, $d[$n++]) = split(" ");
}
$pi = join("",@d);
$k = 0;
while (1) {
    last if ($pos = index($pi, sprintf("%b", $k++))) < 0;
    $out .= $pos +2 . ", ";
}
print $out,"\n";

A038101 First location of palindrome a(n) in decimal expansion of Pi is palindromic.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 99, 141, 151, 313, 343, 505, 535, 585, 767, 959, 1771, 6446, 9669, 15751, 32823, 39193, 48184, 59995, 65456, 73137, 85858, 323323, 944449, 1081801, 1155511, 1299921, 1491941, 5514155, 5870785, 7639367, 7913197, 7940497, 8156518, 8257528

Offset: 1

Patrick De Geest, Feb 15 1999

'Location' starts from the first digit after the decimal point and refers to the first digit of the palindrome.

Dave Andersen, The Pi-Search Page
Patrick De Geest, World!Of Numbers

Cf. A014777, A038099, A038100.

Offset changed to 1 by and more terms from Jinyuan Wang, Sep 04 2021

A061073 First occurrence of n consecutive n's in the decimal expansion of Pi.

Original entry on oeis.org

1, 135, 1698, 54525, 24466, 252499, 3346228, 46663520, 564665206

Offset: 1

Jason Earls, May 27 2001

			1 first occurs at position 1 after the decimal point.
22 first occurs at position 135.
333 first occurs at position 1698.
10101010101010101010 does not occur in the first 1.1*10^10 digits of Pi - _Eric W. Weisstein_, Jul 19 2013

D. Anderson, The Pi-Search Page
Eric Weisstein's World of Mathematics, Earls Sequence
Eric Weisstein's World of Mathematics, Pi Digits

Cf. A014777.

a(9) from Eric W. Weisstein, Jan 16 2006

Entry revised by Don Reble, Apr 06 2006

A082591 Starting position of the first occurrence of n in the decimal expansion of Pi such that a(n) > a(n-1) for n >= 1.

Original entry on oeis.org

32, 37, 53, 64, 70, 90, 98, 99, 101, 122, 163, 174, 220, 281, 295, 314, 396, 428, 446, 495, 600, 650, 661, 698, 803, 822, 841, 977, 1090, 1124, 1358, 1435, 1501, 1667, 1668, 1719, 1828, 1926, 1968, 1987, 2007, 2161, 2210, 2236, 2261, 2305, 2416, 2509, 2555

Offset: 0

Rick L. Shepherd, May 13 2003

a(m)=c means that c + digit_length(m) - 1 is the minimal number of decimal digits of Pi after the decimal point containing all m+1 digit strings 0, 1, 2, ..., m in increasing order from left-to-right (with intervening digit strings of course) - but with some strings overlapping if m >= 34. a(10)=163 ==> 163+2-1=164 digits are necessary to contain in the 11 strings 0, 1, 2, ..., 10 in order.

			a(0) = 32, the position of the first 0 in the decimal expansion of Pi.
a(1) = 37, the position of the first 1 after the first 0.
a(33) = 1667, the starting position of the first string 33 such that
a(33) > a(32)=1501. a(34) = 1668, the starting position of the first string 34
such that a(34) > a(33)=1667. Note that these occurrences of 33 and 34 overlap.

Dave Andersen, Pi-Search Page
Eric Weisstein's World of Mathematics, Pi Digits.

Cf. A014777 (position of first n).

A100080 Position of first occurrence of n after the decimal point in the decimal expansion of 1/Pi.

Original entry on oeis.org

5, 2, 26, 1, 29, 19, 9, 13, 3, 6, 297, 64, 50, 385, 45, 18, 116, 65, 2, 41, 393, 102, 85, 125, 35, 93, 26, 86, 32, 43, 4, 1, 92, 58, 59, 69, 126, 12, 165, 151, 36, 717, 437, 196, 226, 29, 60, 160, 46, 55, 30, 112, 25, 19, 108, 90, 105, 134, 123, 70, 88, 9, 446, 149, 236, 511

Offset: 0

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 03 2004

a(0) = A133268(1),
a(1) = A134251(1),
a(2) = A134252(1),
a(3) = A134253(1),
a(4) = A134254(1),
a(5) = A134255(1),
a(6) = A134256(1),
a(7) = A134257(1),
a(8) = A134258(1),
a(9) = A134259(1),
a(10) = A134260(1). - Artur Jasinski, Oct 16 2007

			1/Pi = 0.31830988618379067153776752674... so the first occurrence of 0 after the decimal point is at position 5; first occurrence of 1 is at position 2; first occurrence of 2 is at position 26; etc.

Cf. A032445 and A014777 for Pi, A078197 for e. Digits of 1/Pi=A049541.

Cf. A037000, A014777, A133268, A134251, A134252, A134253, A134254, A134255, A134256, A134257, A134258, A134259, A134260.

Table[ SequencePosition[#, IntegerDigits@ n][[1, 1]], {n, 0, 65}] &@ First@ RealDigits@ N[1/Pi, 10^4] (* James C. McMahon, Feb 06 2024 *)

Edited by N. J. A. Sloane, Jun 30 2008 at the suggestion of R. J. Mathar

A101196 Position of n-th n after the decimal point in Pi.

Original entry on oeis.org

1, 16, 17, 36, 48, 72, 96, 74, 55, 854, 709, 1080, 1076, 1636, 1657, 1651, 889, 1674, 1227, 2039, 1486, 2372, 2690, 2288, 2033, 2282, 1785, 2703, 4155, 3102, 3584, 3767, 4325, 3808, 3551, 4081, 3785, 3229, 4464, 4884, 4127, 4228, 5336, 3961, 4242, 3633

Offset: 1

Michael Joseph Halm, Dec 12 2004

			a(2) = 16 because the second occurrence of 2 in the digits of pi after its decimal point is at position 16, that is, after 141592653589793.

Cf. A014777, A037000, A037001, A037002, A037003, A037004, A037005, A037006, A037007, A037008.

Corrected and extended by Mark Hudson (mrmarkhudson(AT)hotmail.com), Dec 13 2004

cp's OEIS Frontend

A128050 Position of start of first occurrence of prime(n) after the decimal point in expansion of golden ratio phi.

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A133268 a(n) = positions of 0's after decimal point in decimal expansion of 1/Pi.

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A134210 Positions of 10 after the decimal point in the decimal expansion of Pi.

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A256521 Table T(n, k) of positions p[i] where number n occurs after the decimal point in the decimal expansion of Pi, read by antidiagonals.

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A332929 Position where the binary expansion of n occurs for the first time in the binary expansion of Pi.

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Perl

A038101 First location of palindrome a(n) in decimal expansion of Pi is palindromic.

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A061073 First occurrence of n consecutive n's in the decimal expansion of Pi.

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A082591 Starting position of the first occurrence of n in the decimal expansion of Pi such that a(n) > a(n-1) for n >= 1.

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A100080 Position of first occurrence of n after the decimal point in the decimal expansion of 1/Pi.

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