A078197 Position of the start of the first occurrence of n after the decimal point in e = 2.71828182845904523536...

13, 2, 4, 17, 10, 11, 20, 1, 3, 12, 195, 200, 370, 27, 223, 201, 94, 88, 2, 108, 111, 87, 252, 16, 33, 92, 30, 62, 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

Author

Amarnath Murthy, Nov 21 2002

Keywords

• base
• nonn

Examples

			a(3) = 17 as 3 first occurs in the 17th place after decimal in e. a(18) = 2 = a(182).
		

Links

• T. D. Noe, Table of n, a(n) for n=0..9999

Crossrefs

Cf. A001113, A014777, A143504.

Programs

Magma

k := 400; R := RealField(k); [ Position(IntegerToString(Round(10^k*(-2 + Exp(elt)))), IntegerToString(n)) : n in [0..62] ]; /* Klaus Brockhaus, Feb 15 2007 */

Mathematica

With[{estr=ToString[FromDigits[Rest[RealDigits[E,10,500][[1]]]]]}, Transpose[ Table[First[StringPosition[estr,ToString[n]]],{n,0,80}]][[1]]]  (* Harvey P. Dale, Dec 20 2010 *)
With[{ee=Rest[RealDigits[E,10,500][[1]]]},Transpose[ Flatten[ Table[ SequencePosition[ee,IntegerDigits[ n],1],{n,0,70}],1]][[1]]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, Mar 17 2016 *)

Python

from sympy import E
digits_of_e = str(E.n(10**5))[1:-1] # raise to 10**6 for b-file
def a(n):
    nloc = digits_of_e.find(str(n))
    assert nloc > 0, ("Increase precision", n)
    return nloc
print([a(n) for n in range(63)]) # Michael S. Branicky, Jul 10 2022

Extensions

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 01 2004