A088576 -id:A088576 - cp's OEIS frontend

A036900 Scan decimal expansion of e until all n-digit strings have been seen; a(n) is last string seen.

6, 12, 548, 1769, 92994, 513311, 1934715, 56891305

Offset: 1

The digits scanned are {2, 7, 1, 8, 2, 8, ...}, so the initial 2 in 2.71828... is included and counted as the first digit.

Eric Weisstein's World of Mathematics, Constant Digit Scanning
Eric Weisstein's World of Mathematics, e Digits

Cf. A001113 (decimal expansion of e).
Cf. A036904 (number of digits in the decimal expansion of e that must be scanned to get all n-digit number).
Cf. A088576 (starting position of the first occurrence of n in the decimal expansion of e).
Cf. A036901, A036902, A036903, A036905, A036906.

a(7) = 1934715 from Eric W. Weisstein, Sep 10 2013

a(8) = 56891305 from Eric W. Weisstein, Sep 11 2013

A051238 First appearance of string n in e.

Original entry on oeis.org

3, 1, 18, 11, 12, 21, 2, 4, 13, 196, 201, 371, 28, 224, 202, 95, 89, 3, 109, 112, 88, 253, 17, 34, 93, 31, 1, 5, 132, 72, 190, 111, 143, 144, 18, 20, 271, 86, 107, 67, 125, 98, 135, 240, 11, 104, 26, 229, 35, 236, 94, 16, 19, 77, 302, 154, 39, 326, 12, 21

Offset: 1

Harvey P. Dale

A088576 has the a(0) term.

T. D. Noe, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, e Digits

Cf. A001113 (decimal expansion of e).
Cf. A088576 (same as a(n) but including the term for n = 0).
Cf. A032445.

(* Computing 200000 digits of e is sufficient up to n=10000 *) eString = RealDigits[E, 10, 200000] // First // ToString /@ # & // StringJoin; a[n_] := (p = StringPosition[eString, n // ToString, 1]; If[p == {}, 0, p[[1, 1]]]); Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Mar 04 2013 *)
With[{eee=RealDigits[E,10,200000][[1]]},Transpose[Flatten[Table[ SequencePosition[ eee,IntegerDigits[n],1],{n,70}],1]][[1]]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, Nov 20 2015 *)

A036904 Scan decimal expansion of e until all n-digit strings have been seen; a(n) is number of digits that must be scanned.

Original entry on oeis.org

21, 372, 8092, 102128, 1061613, 12108841, 198150341, 1929504534

Offset: 1

Michael Kleber

The digits scanned are {2, 7, 1, 8, 2, 8, ...}, so the initial 2 in 2.71828... is included and counted as the first digit.

Eric Weisstein's World of Mathematics, Constant Digit Scanning
Eric Weisstein's World of Mathematics, e Digits

Cf. A001113 (decimal expansion of e).
Cf. A036900 (last number encountered when scanning the decimal expansion of e for all n-digit strings).
Cf. A088576 (starting positions of the first occurrence of n in the decimal expansion of e).
Cf. A032510, A036900-A036906.

a(7) from Piotr Idzik, Nov 01 2011

a(8) from Eric W. Weisstein, Sep 11 2013

A281092 Position of the first occurrence of n in the decimal expansion of e.

Original entry on oeis.org

13, 2, 0, 17, 10, 11, 20, 1, 3, 12, 195, 200, 370, 27, 223, 201, 94, 88, 2, 108, 111, 87, 252, 16, 33, 92, 30, 0, 4, 131, 71, 189, 110, 142, 143, 17, 19, 270, 85, 106, 66, 124, 97, 134, 239, 10, 103, 25, 228, 34, 235, 93, 15, 18, 76, 301, 153, 38, 325, 11, 20, 242, 32

Offset: 0

Bobby Jacobs, Jan 21 2017

The 2 before the decimal point is counted as position 0.

This differs from A078197(n) at n = 2, 27, 271, 2718, ... .

Cf. A001113, A051238, A078197, A088576, A176341.

With[{ed=RealDigits[E,10,500][[1]]},Flatten[Table[SequencePosition[ ed, IntegerDigits[n],1][[All,1]],{n,0,65}]]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 06 2017 *)

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

Zhining Yang, Mar 11 2025

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

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

Zhining Yang, Table of n, a(n) for n = 0..9999

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).

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}]

cp's OEIS Frontend

A036900 Scan decimal expansion of e until all n-digit strings have been seen; a(n) is last string seen.

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A051238 First appearance of string n in e.

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A036904 Scan decimal expansion of e until all n-digit strings have been seen; a(n) is number of digits that must be scanned.

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A281092 Position of the first occurrence of n in the decimal expansion of e.

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Mathematica

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

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Mathematica