A014777 -id:A014777 - cp's OEIS frontend

A134215 Positions of 15 after decimal point in decimal expansion of Pi.

3, 314, 324, 344, 393, 730, 922, 1030, 1098, 1100, 1114, 1315, 1342, 1436, 1657, 2148, 2150, 2215, 2327, 2389, 2501, 2565, 2688, 2957, 3000, 3093, 3099, 3275, 3280, 3354, 3414, 3464, 3522, 3532, 3553, 3644, 3858, 3959, 4362, 4389, 4536, 4597, 4645, 4828, 4866

Offset: 1

Artur Jasinski, Oct 14 2007

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

Cf. A037008, A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037007, A014777, A050208, A134212, A134213, A134214, A134216, A134217, A134218, A134218, A134219.

First /@ SequencePosition[RealDigits[Pi - 3, 10, 5000][[1]], {1, 5}] (* Amiram Eldar, Mar 20 2020 *)

More terms from Amiram Eldar, Mar 20 2020

A134216 Positions of 16 after decimal point in decimal expansion of Pi.

Original entry on oeis.org

40, 68, 238, 396, 791, 992, 1130, 1182, 1206, 1324, 1410, 1422, 1504, 1602, 1610, 1651, 1709, 1767, 2142, 2185, 2345, 2352, 2402, 2459, 2640, 2746, 3024, 3220, 3370, 3399, 3409, 3516, 3529, 3535, 3585, 3650, 3660, 3860, 3978, 3994, 4128, 4342, 4385, 4648, 4653

Offset: 1

Artur Jasinski, Oct 14 2007

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

Cf. A037008, A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037007, A014777, A050208, A134212, A134213, A134214, A134215, A134217, A134218, A134218, A134219.

First /@ SequencePosition[RealDigits[Pi - 3, 10, 5000][[1]], {1, 6}] (* Amiram Eldar, Mar 20 2020 *)

More terms from Amiram Eldar, Mar 20 2020

A134217 Positions of 17 after decimal point in decimal expansion of Pi.

Original entry on oeis.org

95, 138, 155, 319, 342, 428, 438, 547, 566, 568, 574, 640, 646, 786, 850, 887, 889, 961, 1086, 1134, 1152, 1419, 1577, 1621, 1625, 1758, 1788, 1850, 1946, 2109, 2187, 2491, 2573, 2591, 2947, 3177, 3310, 3393, 3419, 3539, 3789, 4094, 4218, 4418, 4430, 4444, 4510

Offset: 1

Artur Jasinski, Oct 14 2007

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

Cf. A037008, A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037007, A014777, A050208, A134212, A134213, A134214, A134215, A134216, A134218, A134218, A134219.

Flatten[Position[Partition[Rest[RealDigits[\[Pi],10,3000][[1]]],2,1], {1,7}]]  (* Harvey P. Dale, Apr 07 2011 *)

More terms from Harvey P. Dale, Apr 07 2011

More terms from Amiram Eldar, Mar 20 2020

A134218 Positions of 18 after decimal point in decimal expansion of Pi.

Original entry on oeis.org

424, 446, 471, 490, 587, 728, 752, 797, 847, 951, 1035, 1056, 1225, 1444, 1539, 1572, 1574, 1674, 1715, 1738, 1897, 2220, 2628, 2776, 2867, 2942, 2964, 2989, 3082, 3149, 3318, 3339, 3343, 3439, 3549, 3596, 3607, 3664, 3801, 3922, 3956, 4044, 4070, 4145, 4179, 4485

Offset: 1

Artur Jasinski, Oct 14 2007

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

Cf. A037008, A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037007, A014777, A050208, A134212, A134213, A134214, A134215, A134216, A134217, A134219.

First /@ SequencePosition[RealDigits[Pi - 3, 10, 5000][[1]], {1, 8}] (* Amiram Eldar, Mar 20 2020 *)

More terms from Amiram Eldar, Mar 20 2020

A134219 Positions of 19 after decimal point in decimal expansion of Pi.

Original entry on oeis.org

37, 168, 198, 246, 390, 417, 432, 495, 541, 704, 717, 843, 945, 975, 985, 997, 1047, 1166, 1227, 1237, 1345, 1384, 1427, 1535, 1618, 1641, 1733, 1881, 1915, 1944, 2054, 2128, 2821, 2856, 2872, 2897, 2902, 2905, 2918, 2944, 2960, 2997, 3030, 3166, 3337, 3358

Offset: 1

Artur Jasinski, Oct 14 2007

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

Cf. A037008, A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037007, A014777, A050208, A134212, A134213, A134214, A134215, A134216, A134217, A134218.

Transpose[SequencePosition[RealDigits[Pi,10,10000][[1]],{1,9}]][[1]]-1 (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, May 09 2016 *)

A037024 Position of start of first occurrence of prime(n) after the decimal point in expansion of Pi.

Original entry on oeis.org

6, 9, 4, 13, 94, 110, 95, 37, 16, 186, 137, 46, 2, 23, 119, 8, 4, 219, 98, 39, 299, 13, 26, 11, 12, 852, 3486, 1487, 206, 362, 297, 1096, 859, 525, 2606, 393, 1657, 1410, 1182, 428, 438, 728, 1944, 168, 37, 704, 93, 135, 484, 185, 229, 1688, 1707, 1713, 1006

Offset: 1

Patrick De Geest, Jan 04 1999

			Pi = 3.14159265358979323846264338327950288... (see A000796).
First occurrence of prime(23) = 83 starts at the 26th digit after the decimal point, hence a(23) = 26.

Michael S. Branicky, Table of n, a(n) for n = 1..10000
Dave Andersen, The Pi-Search Page

Cf. A000796, A014777.

k:=3500; R := RealField(k); [ Position(IntegerToString(Round(10^k*(-3 + Pi(R)))), IntegerToString(NthPrime(n))) : n in [1..55] ]; /* Klaus Brockhaus, Feb 15 2007 */

Module[{p = Rest[First[RealDigits[Pi, 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 *)

from itertools import takewhile
from sympy import S, prime, primerange
# download https://stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt, then
# with open('pi-billion.txt', 'r') as f: pi_digits = f.readline()[1:]
pi_digits = str(S.Pi.n(10**4))[1:] # alternative to above
def aupton(nn):
    plocs = (pi_digits.find(str(p)) for p in primerange(2, prime(nn)+1))
    return list(takewhile(lambda x: x>=0, plocs)) # until p not found
print(aupton(55)) # Michael S. Branicky, Jun 12 2021

Edited by Klaus Brockhaus, Feb 15 2007

A038099 Numbers k such that k > first location of string of k in decimal expansion of Pi.

Original entry on oeis.org

4, 5, 9, 14, 15, 23, 26, 32, 33, 35, 38, 41, 43, 46, 50, 51, 53, 58, 59, 62, 64, 65, 69, 71, 74, 75, 78, 79, 81, 82, 83, 84, 86, 88, 89, 92, 93, 94, 95, 97, 98, 99, 105, 117, 132, 141, 148, 159, 164, 169, 170, 172, 174, 193, 197, 208, 209, 211, 214, 223, 229

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 a(n).

Jinyuan Wang, Table of n, a(n) for n = 1..2000
Dave Andersen, Pi-Search Page

Cf. A000796, A014777, A038100.

from sympy import pi
from itertools import count, islice
digits_of_pi = str(pi.n(10**5))[1:-1]
def agen():
    for k in count(1):
        kloc = digits_of_pi.find(str(k))
        assert kloc > 0, ("Increase precision", k)
        if k > kloc: yield k
print(list(islice(agen(), 61))) # Michael S. Branicky, Jul 10 2022

a(n) > A014777(n). - Michael S. Branicky, Jul 10 2022

Offset changed to 1 by Jinyuan Wang, Sep 04 2021

A038100 Numbers k such that k < first location of string of k in decimal expansion of Pi.

Original entry on oeis.org

0, 2, 3, 6, 7, 8, 10, 11, 12, 13, 16, 17, 18, 19, 20, 21, 22, 24, 25, 27, 28, 29, 30, 31, 34, 36, 37, 39, 40, 42, 44, 45, 47, 48, 49, 52, 54, 55, 56, 57, 60, 61, 63, 66, 67, 68, 70, 72, 73, 76, 77, 80, 85, 87, 90, 91, 96, 100, 101, 102, 103, 104, 106, 107, 108

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 a(n).

Jinyuan Wang, Table of n, a(n) for n = 1..5000
Dave Andersen, The Pi-Search Page

Cf. A000796, A014777, A038099.

from sympy import pi
from itertools import count, islice
digits_of_pi = str(pi.n(10**5))[1:-1]
def agen():
    for k in count(0):
        kloc = digits_of_pi.find(str(k))
        assert kloc > 0, ("Increase precision", k)
        if k < kloc: yield k
print(list(islice(agen(), 65))) # Michael S. Branicky, Jul 10 2022

a(n) < A014777(n). - Michael S. Branicky, Jul 10 2022

Offset changed to 1 by Jinyuan Wang, Sep 04 2021

A103186 a(n) is the position of the start of the first occurrence of n > a(n-1) after the decimal point in Pi = 3.14159265358979323846264338327950288...

Original entry on oeis.org

1, 6, 9, 19, 31, 41, 47, 52, 55, 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, 2595

Offset: 1

Suggested by Bob's Poetry Page. - Alonso del Arte, Mar 01 2005

The digits at position 1667 are "334", so according to the strict definition of this sequence, a(33) is 1667 and a(34) is 1668. However, this would not enable a person to mark in bold-face the counting numbers within the digits of pi, which was the inspiration for this sequence. Surprisingly, if overlapping is not allowed, this changes only one element of the sequence. a(34) becomes 1700 and a(35) remains 1719. No other overlapping occurs within the first 100,000 decimal digits of Pi. - Graeme McRae, Mar 20 2005

			Moving always to the right in the decimal expansion of Pi, the string "1" is found at position 1 counting from the first digit after the decimal point, the string "2" is found at position 6, the string "3" at position 6, the string "4" at position 19, etc.

Robert G. Wilson v, Table of n, a(n) for n = 1..9999
Dave Andersen, The Pi-Search Page.
Bob Happelberg, Bob's Poetry Page for Feb 2005

Cf. A000796, A078197, A014777 (another version).

k := 3000; R := RealField(k); S := IntegerToString(Round(10^k*(-3 + Pi(R)))); Q := []; d := 0; for n in [1..49] do p:= Position(S, IntegerToString(n)); d+:=p; Append(~Q, d); S := Substring(S, p+1, #S-p); end for; Q; /* Klaus Brockhaus, Feb 15 2007 */

p = ToString[ FromDigits[ RealDigits[ N[Pi - 3, 2600]][[1]]]]; lst = {0}; Do[a = StringPosition[p, ToString[n], 1][[1, 1]]; AppendTo[lst, a + lst[[ -1]]]; p = StringDrop[p, a], {n, 49}]; Rest[lst] (* Robert G. Wilson v, Mar 19 2005 *)

lista(nn, t=10^5) = {default(realprecision, t); my(d, k, v=digits(floor(Pi*10^t))); for(n=1, nn, d=digits(n); until(v[k+1..k+#d]==d, k++); print1(k, ", ")); } \\ Jinyuan Wang, Feb 18 2021

More terms from Graeme McRae and Robert G. Wilson v, Mar 19 2005

A178707 Position of the start of the first occurrence of n (expressed in binary) after the binary point in the binary expansion of Pi.

Original entry on oeis.org

1, 3, 3, 11, 3, 16, 15, 11, 6, 3, 19, 16, 47, 15, 14, 11, 6, 25, 3, 60, 23, 19, 16, 91, 47, 76, 18, 15, 93, 14, 13, 11, 95, 6, 25, 43, 3, 126, 60, 144, 23, 58, 19, 393, 227, 16, 91, 207, 47, 63, 245, 76, 40, 18, 15, 103, 93, 114, 184, 14, 173, 13, 12, 11, 95

Offset: 0

Will Nicholes, Jun 06 2010

			The first nonnegative integer is 0; its binary expansion is 0, which is found at the first digit after Pi's binary point; therefore the first term in the sequence is "1".
The sixth nonnegative integer is 5; its binary expansion is 101, which is found starting at the 16th digit after Pi's binary point; therefore the sixth term in the sequence is "16".

Cf. A004601, A014777.

cp's OEIS Frontend

A134215 Positions of 15 after decimal point in decimal expansion of Pi.

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A134216 Positions of 16 after decimal point in decimal expansion of Pi.

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A134217 Positions of 17 after decimal point in decimal expansion of Pi.

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A134218 Positions of 18 after decimal point in decimal expansion of Pi.

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A134219 Positions of 19 after decimal point in decimal expansion of Pi.

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Mathematica

A037024 Position of start of first occurrence of prime(n) after the decimal point in expansion of Pi.

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A038099 Numbers k such that k > first location of string of k in decimal expansion of Pi.

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A038100 Numbers k such that k < first location of string of k in decimal expansion of Pi.

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A103186 a(n) is the position of the start of the first occurrence of n > a(n-1) after the decimal point in Pi = 3.14159265358979323846264338327950288...