cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A068394 Numbers k such that the k-th digit of Pi and the k-th digit of e are the same.

Original entry on oeis.org

12, 16, 17, 20, 33, 39, 44, 55, 58, 69, 80, 94, 99, 142, 169, 205, 243, 262, 274, 278, 293, 323, 325, 330, 333, 360, 364, 387, 388, 395, 411, 419, 427, 428, 452, 459, 460, 461, 483, 493, 499, 500, 503, 506, 511, 522, 525, 547, 581, 590, 594, 595, 598, 602
Offset: 1

Views

Author

Benoit Cloitre, Mar 08 2002

Keywords

Examples

			Let dPi(n) be the n-th digit of Pi=3.14159... (e.g., dPi(2)=4) and de(n) be the n-th digit of e=2.718... (e.g., de(2)=1); then dPi(12) = de(12) = 9, hence 12 is in the sequence.

Links

Crossrefs

Cf. A000796, A001113, A052055.

Programs

  • Magma
    m:=610; p:=Pi(RealField(m+1)); sp:=IntegerToString(Round(10^m*(p-3))); e:=Exp(One(RealField(m+1))); se:=IntegerToString(Round(10^m*(e-2))); [ a: a in [1..m] | sp[a] eq se[a] ]; // Klaus Brockhaus, Sep 04 2009
  • Mathematica
    max = 600; Position[RealDigits[Pi - 3, 10, max][[1]] - RealDigits[E - 2, 10, max][[1]], ?(# == 0 &)] // Flatten (* _Amiram Eldar, May 21 2022 *)

Formula

a(n) = A052055(n) - 1.

Extensions

Listed terms verified by Klaus Brockhaus, Sep 04 2009

A257492 Positions where Pi and the Golden Ratio have a common decimal digit.

Original entry on oeis.org

13, 15, 19, 43, 46, 49, 53, 60, 64, 66, 71, 78, 100, 102, 107, 108, 114, 134, 138, 139, 140, 158, 162, 170, 171, 173, 177, 178, 185, 191, 196, 230, 240, 254, 271, 290, 304, 314, 322, 360, 368, 395, 396, 402, 407, 416, 437, 439, 440, 443, 448, 465, 468, 472
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2015

Keywords

Crossrefs

Cf. A052055, A257494.

Programs

  • Mathematica
    With[{nn=1000},Flatten[Position[Thread[{RealDigits[GoldenRatio,10,nn][[1]],RealDigits[Pi,10,nn][[1]]}],_?(#[[1]]==#[[2]]&),{1},Heads-> False]]]
  • Python
    from sympy import S
digits = 1000
pi, phi = str(S.Pi.n(digits+3)), str(S.GoldenRatio.n(digits+3))
print([k for k in range(2, digits+1) if pi[k] == phi[k]]) # Michael S. Branicky, May 06 2023

A257494 Positions where e and the Golden Ratio have a common decimal digit.

Original entry on oeis.org

3, 4, 10, 13, 24, 29, 32, 37, 38, 62, 63, 65, 100, 101, 127, 132, 150, 159, 170, 180, 183, 194, 204, 216, 228, 239, 256, 260, 268, 273, 277, 289, 297, 300, 310, 319, 320, 341, 375, 385, 391, 396, 406, 430, 431, 458, 473, 476, 486, 493, 500, 536, 544, 549
Offset: 1

Views

Author

Harvey P. Dale, Apr 26 2015

Keywords

Crossrefs

Cf. A001113, A001622.
Cf. A052055, A257492.

Programs

  • Mathematica
    With[{nn=1000},Flatten[Position[Thread[{RealDigits[GoldenRatio,10,nn][[1]],RealDigits[E,10,nn][[1]]}],_?(#[[1]]==#[[2]]&),{1},Heads-> False]]]

A242973 Positions in both e and Pi where both digits in the same position are prime.

Original entry on oeis.org

1, 5, 9, 16, 17, 18, 25, 29, 30, 34, 40, 54, 64, 65, 74, 77, 84, 90, 92, 94, 100, 103, 112, 115, 124, 132, 136, 137, 138, 143, 144, 159, 178, 179, 180, 195, 204, 211, 217, 236, 242, 253, 275, 283, 286, 293, 302, 303, 305, 307, 317, 321, 326, 334, 339, 344, 347
Offset: 1

Views

Author

Philip Mizzi, May 28 2014

Keywords

Examples

			Pi = 3.1415926535897932384626...
.....|....|...|......|||........
_e = 2.7182818284590452353602...

Links

Crossrefs

Cf. A052055, A073302, A153031.

Programs

  • Mathematica
    Module[{digs=350,p,e,th},p=RealDigits[Pi,10,digs][[1]];e=RealDigits[E,10,digs][[1]];th = Thread[{p,e}];Position[If[AllTrue[#,PrimeQ],1,0]&/@th,1]]//Flatten (* Harvey P. Dale, Jan 28 2023 *)
  • PARI
    \p 1000
e=Vec(Str(exp(1)/10)); p=Vec(Str(Pi/10)); for(n=1, #e-9, if(isprime(eval(e[n+2])) && isprime(eval(p[n+2])), print1(n", "))) \\ Jens Kruse Andersen, Jul 23 2014

Extensions

Definition clarified by Harvey P. Dale, Jan 28 2023

A242975 Positions in e and Pi where the digit at each position is equal and prime.

Original entry on oeis.org

17, 18, 34, 40, 100, 143, 275, 326, 334, 365, 412, 420, 453, 501, 504, 507, 610, 622, 642, 743, 825, 840, 841, 864, 866, 875, 878, 898, 920, 926, 941, 948, 956, 963, 1009, 1054, 1059, 1078, 1147, 1158, 1180, 1203, 1283, 1292, 1306, 1338, 1355, 1362, 1407, 1469
Offset: 1

Views

Author

Philip Mizzi, May 28 2014

Keywords

Examples

			Pi = 3.1415926535897932384626...
......................||........
_e = 2.7182818284590452353602...

Links

Crossrefs

Cf. A052055, A153031, A242973.

Programs

A381980 a(n) is the first position where the digits of n occur simultaneously in the decimal expansions of Pi and e.

Original entry on oeis.org

331, 95, 17, 18, 263, 326, 21, 40, 206, 13, 13422, 428, 500, 6426, 12896, 11172, 17951, 962, 9710, 2857, 9261, 4782, 21688, 17, 26172, 2526, 2060, 2900, 5375, 6167, 10097, 13009, 9287, 12651, 4175, 840, 38691, 11997, 14119, 3519, 4684, 21785, 7662, 1798, 1253, 10869, 9157, 7216, 3430, 13191, 5148, 1843, 10790
Offset: 0

Views

Author

Zhining Yang, Mar 11 2025

Keywords

Comments

The digits of the decimal expansions are numbered starting with 1 at the initial digits 3 (resp. 2).

Examples

			a(9) = 13 because the first "9" appears simultaneously in Pi and e at index 13:
Pi = 3.1415926535897932384626...
     . ...........|.............
 e = 2.7182818284590452353602...

Links

Crossrefs

Cf. A000796 (Pi), A001113 (e).
Cf. A032445 (positions in Pi), A088576 (positions in e).
Cf. A052055 (positions in both Pi and e indicate a common digit).

Programs

  • Mathematica
    pi=RealDigits[Pi,10,40000][[1]];
e=RealDigits[E,10,40000][[1]];
Table[Intersection[SequencePosition[pi,IntegerDigits[k]][[All,1]],SequencePosition[e,IntegerDigits[k]][[All,1]]][[1]],{k,0,52}]
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.