A037001 -id:A037001 - cp's OEIS frontend

A014777 Position of the start of the first occurrence of n after the decimal point in Pi = 3.14159265358979323846264338327950288...

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, 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

Offset: 0

Paul Simon (paulsimn(AT)microtec.net) and Simon Plouffe

This is A037008(1), A037000(1), A037001(1), A037002(1), A037003(1), A037004(1), A037005(1), A036974(1), A037006(1), A037007(1) etc.

			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 "1" is found at position 1, the string "2" at position 6, the string "3" at position 9, etc.

Ronald R. King and T. D. Noe, Table of n, a(n) for n = 0..9999
Dave Andersen, The Pi-Search Page.
Tom Crawford and Brady Haran, Strings and Loops within Pi, Numberphile video (2020)
Anders Hellström, Sage program, Feb 02 2017

Cf. A000796, A078197, A103186 (another version).

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

k := 700; R := RealField(k); [ Position(IntegerToString(Round(10^k*(-3 + Pi(R)))), IntegerToString(n)) : n in [0..68] ]; /* Klaus Brockhaus, Feb 15 2007 */

Table[-1 + SequencePosition[#, IntegerDigits@ n][[1, 1]], {n, 0, 68}] &@ First@ RealDigits@ N[Pi, 10^4] (* Michael De Vlieger, Aug 10 2016, Version 10.1 *)

M14777=Map(); A014777(n)={iferr(mapget(M14777, n), E, my(i=if(n>9, A014777(n\10), 1), d=if(n, digits(n), [0]), j); while(i++, j=#d; until(!j, d[j]==A000796(i+j--) || next(2)); break); mapput(M14777, n, i--); i)} \\ M. F. Hasler, Jun 21 2022

from mpmath import mp
def A014777(n):
    if not (i := A014777.pos.get(n, 0)):
        d = str(n); s = 2 # starting position for search
        while (i := A014777.pi.find(d, s)) < 1:
            s = max(len(A014777.pi) - len(d), 2)
            with mp.workdps(s + 99 if s < 500 else s*6//5): # new precision
                A014777.pi = str(mp.pi - 5/mp.mpf(10)**mp.dps) # don't round
        i -= 1; A014777.pos[n] = i
    return i
A014777.pi = ''; A014777.pos = {} # M. F. Hasler, Jun 21 2022

More terms from Klaus Brockhaus, Feb 15 2007

A037000 Positions of the digit '1' in the decimal expansion of Pi.

Original entry on oeis.org

1, 3, 37, 40, 49, 68, 94, 95, 103, 110, 138, 148, 153, 154, 155, 163, 168, 174, 175, 198, 206, 220, 238, 243, 246, 250, 269, 281, 295, 297, 314, 319, 324, 342, 344, 362, 363, 381, 385, 390, 393, 395, 396, 417, 424, 427, 428, 432, 437, 438, 442, 445, 446

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

From M. F. Hasler, Jul 28 2024: (Start)
"Positions" are indices n of digits d(n) such that Pi = Sum_{n >= 0} d(n)/10^n; see A053745 for the variant where the initial digit 3 is at position 1.
The first few primes in this sequence are 3, 37, 103, 163, 269, 281, 499, 541, 547, 587, 607, 709, 797, 859, 887, 971, 983, 997, ... (End)

Robert Israel, Table of n, a(n) for n = 1..10137
Eric Weisstein's World of Mathematics, Pi Digits

Cf. A000796 (decimals of Pi), A037001 - A037008 and A036974 (positions of other digits), A053745 (variant with all values increased by 1).

P:= convert(evalf[100000](Pi),string)[3..-1]:
select(t -> P[t]="1",[$1..length(P)-1]); # Robert Israel, Dec 22 2013

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 1] (* Robert G. Wilson v, Mar 07 2011 *)

A037000_upto(N=500, d=1)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)], N[i]==d]} \\ M. F. Hasler, Jul 28 2024

Conjecturally, a(n) ~ 10n.

A037008 Positions of the digit '0' in the decimal expansion of Pi, where positions 0, 1, 2, ... correspond to digits 3, 1, 4, ....

Original entry on oeis.org

32, 50, 54, 65, 71, 77, 85, 97, 106, 116, 121, 128, 132, 146, 159, 164, 167, 176, 195, 207, 245, 248, 264, 270, 287, 291, 307, 308, 311, 327, 330, 340, 357, 360, 361, 366, 369, 375, 398, 403, 408, 421, 443, 451, 493, 513, 520, 523, 543, 545, 552, 557, 561

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

			Pi = 3.14159 26535 89793 23846 26433 83279 5*0*288 4... (Position 32 refers to the 32nd digit after the decimal point.)

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..369 from M. F. Hasler)
Eric Weisstein's World of Mathematics, Pi Digits.

Cf. A000796 (decimal expansion (or digits) of Pi).
For another version see A014976(n) = a(n) + 1.
For digits 0 through 9 see: this sequence, A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037007.

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 0] (* Robert G. Wilson v, Mar 07 2011 *)

for(c=1,default(realprecision,2011)-2,Pi\.1^c%10 || print1(c",")) \\ M. F. Hasler, Oct 23 2011

A037008_upto(N=999)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)],!N[i]]} \\ M. F. Hasler, Jul 29 2024

a(n) = A014976(n) - 1. - M. F. Hasler, Jul 29 2024

Name edited by M. F. Hasler, Jul 29 2024

A037007 Positions of the digit '9' in the decimal expansion of Pi, where positions 0, 1, 2,... correspond to digits 3, 1, 4, ....

Original entry on oeis.org

5, 12, 14, 30, 38, 42, 44, 45, 55, 58, 62, 79, 80, 100, 122, 129, 144, 169, 180, 187, 190, 193, 199, 208, 214, 247, 249, 259, 284, 294, 328, 331, 336, 341, 353, 356, 388, 391, 399, 414, 416, 418, 422, 433, 440, 459, 460, 465, 482, 487, 496, 498, 501, 527

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

Primes in this sequence are 5, 79, 193, 199, 331, 353, 433, 487, 941, ... - M. F. Hasler, Jul 29 2024

			The first digit '9' occurs in 3.1415926... at the 5th place after the decimal point, whence a(1) = 5.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..369 from M. F. Hasler)
Eric Weisstein's World of Mathematics, Pi Digits.
Index entries for sequences related to the number Pi

Cf. A000796 (decimals of Pi).
Cf. A053753 (variant with all values increased by 1).
Cf. A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037008 (similar for digits 1, ..., 8 and 0).
Cf. A048940, A096763 (starting position of at least/exactly n '9's).

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 9] (* Robert G. Wilson v, Mar 07 2011 *)

A037007_upto(N=999, d=9)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)], N[i]==d]} \\ M. F. Hasler, Jul 29 2024

a(n) = A053753(n) - 1. - M. F. Hasler, Mar 20 2017

a(n) ~ 10*n if Pi is normal (as generally assumed, but yet unproved). - M. F. Hasler, Jul 29 2024

A036974 Positions of the digit '7' in decimal expansion of Pi.

Original entry on oeis.org

13, 29, 39, 47, 56, 66, 96, 99, 120, 139, 156, 166, 209, 224, 232, 235, 242, 288, 299, 301, 306, 320, 343, 351, 405, 407, 412, 429, 439, 452, 458, 463, 468, 475, 478, 486, 506, 538, 540, 544, 548, 556, 559, 560, 567, 569, 575, 577, 584, 591, 609, 621, 622

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

In the first 400 digits of Pi, 7 is rare and only appears 24 times. In the next 250 digits of Pi, 7 is common and appears 38 times. - Bobby Jacobs, Oct 18 2016

			3.141592653589(7)932384626433832(7)950288419(7)1693993(7)510
58209(7)494459230(7)81640628620899862803482534211(7)06(7)9
8214808651328230664(7)093844609550582231(7)25359408128
48111(7)450284102(7)0193852110555964462294895493038196
44288109(7)56659334461284(7)5648233(7)86(7)831652(7)12019091
4564856692346034861045432664821339360(7)2602491412(7)3
(7)2458(7)0066063155881(7)4881520920962829254091(7)1536436
(7)8925903600113305305488204665213841469519415116094
3305(7)2(7)0365(7)5959195309218611(7)381932611(7)93105118548
0(7)44623(7)9962(7)4956(7)351885(7)52(7)2489122(7)93818301194912
98336(7)3362440656643086021394946395224(7)3(7)190(7)021(7)98
60943(7)02(77)053921(7)1(7)62931(7)6(7)523846(7)481846(7)669405132
00056812(7)14526356082(77)85(77)1342(7)5(77)896091(7)363(7)1(7)8(7)...

Amiram Eldar, Table of n, a(n) for n = 1..10000
Bobby Jacobs, Pirotechnics
Eric Weisstein's World of Mathematics, Pi Digits

Cf. A000796.

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

Flatten@Position[RealDigits[Pi - 3, 10, 500][[1]], 7] (* Robert G. Wilson v,Mar 07 2011 *)
Union[Flatten[SequencePosition[RealDigits[Pi,10,700][[1]],{7}]]]-1 (* Harvey P. Dale, Jul 13 2023 *)

A037002 Positions of the digit '3' in the decimal expansion of Pi - 3.

Original entry on oeis.org

9, 15, 17, 24, 25, 27, 43, 46, 64, 86, 91, 111, 115, 123, 137, 142, 170, 194, 196, 215, 216, 230, 231, 237, 261, 265, 274, 282, 283, 285, 300, 313, 346, 349, 358, 364, 365, 368, 382, 401, 402, 409, 420, 430, 434, 441, 457, 469, 488, 492, 503, 504, 507, 508

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

Amiram Eldar, Table of n, a(n) for n = 1..10000
Dave Andersen, The Pi-Search page, angio.net, since 1996, updated 2013.
Eric Weisstein's World of Mathematics, Pi Digits.

Cf. A000796, A036974, A037000, A037001, A037003, A037004, A037005, A037006, A037007, A037008.

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 3] (* Robert G. Wilson v, Mar 07 2011 *)

A037003 Positions of the digit '4' in the decimal expansion of Pi.

Original entry on oeis.org

2, 19, 23, 36, 57, 59, 60, 70, 87, 92, 104, 119, 125, 126, 145, 151, 157, 162, 182, 183, 188, 192, 201, 202, 217, 218, 223, 227, 251, 254, 262, 266, 271, 273, 278, 293, 296, 303, 321, 339, 348, 371, 376, 384, 386, 392, 400, 449, 453, 454, 464, 480, 497, 511

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pi Digits.

Cf. A036974.

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

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 4] (* Robert G. Wilson v, Mar 07 2011 *)

A037004 Positions of the digit '5' in the decimal expansion of Pi.

Original entry on oeis.org

4, 8, 10, 31, 48, 51, 61, 90, 109, 130, 131, 133, 141, 143, 158, 172, 177, 178, 179, 191, 210, 213, 225, 240, 252, 256, 272, 304, 315, 316, 325, 338, 345, 355, 367, 370, 379, 389, 394, 404, 411, 413, 415, 419, 444, 448, 466, 470, 474, 476, 515, 534, 562

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pi Digits.

Cf. A036974.

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

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 5] (* Robert G. Wilson v, Mar 07 2011 *)

A037005 Positions of the digit '6' in the decimal expansion of Pi.

Original entry on oeis.org

7, 20, 22, 41, 69, 72, 75, 82, 98, 108, 117, 118, 127, 181, 184, 200, 211, 212, 219, 226, 234, 239, 253, 257, 258, 263, 268, 276, 277, 286, 290, 309, 310, 312, 332, 347, 350, 359, 377, 378, 387, 397, 410, 426, 436, 455, 461, 467, 505, 509, 514, 516, 517

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pi Digits.

Cf. A036974.

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

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 6] (* Robert G. Wilson v, Mar 07 2011 *)

A037006 Positions of the digit '8' in the decimal expansion of Pi.

Original entry on oeis.org

11, 18, 26, 34, 35, 52, 67, 74, 78, 81, 84, 88, 101, 105, 107, 113, 124, 134, 147, 150, 152, 161, 171, 189, 197, 204, 205, 222, 228, 233, 236, 255, 267, 279, 305, 317, 318, 322, 323, 334, 352, 372, 373, 383, 425, 431, 447, 450, 472, 473, 481, 489, 491, 502

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

Amiram Eldar, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pi Digits.

Cf. A036974.

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

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 8] (* Robert G. Wilson v, Mar 07 2011 *)

cp's OEIS Frontend

A014777 Position of the start of the first occurrence of n after the decimal point in Pi = 3.14159265358979323846264338327950288...

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A037000 Positions of the digit '1' in the decimal expansion of Pi.

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A037008 Positions of the digit '0' in the decimal expansion of Pi, where positions 0, 1, 2, ... correspond to digits 3, 1, 4, ....

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A037007 Positions of the digit '9' in the decimal expansion of Pi, where positions 0, 1, 2,... correspond to digits 3, 1, 4, ....

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A036974 Positions of the digit '7' in decimal expansion of Pi.

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A037002 Positions of the digit '3' in the decimal expansion of Pi - 3.

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A037003 Positions of the digit '4' in the decimal expansion of Pi.

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A037004 Positions of the digit '5' in the decimal expansion of Pi.

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