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

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

Author

Benoit Cloitre, Mar 08 2002

Keywords

• easy
• nonn
• base

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

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..290 from Carmine Suriano)

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