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

1,1

Links

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

Formula

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

Example

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.

Mathematica

max = 600; Position[RealDigits[Pi - 3, 10, max][[1]] - RealDigits[E - 2, 10, max][[1]], _?(# == 0 &)] // Flatten (* Amiram Eldar, May 21 2022 *)

Prog

(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

Crossrefs

Cf. A000796, A001113, A052055.

Sequence in context: A175784 A143090 A328074 * A189685 A126763 A058080

Adjacent sequences: A068391 A068392 A068393 * A068395 A068396 A068397

Keyword

easy,nonn,base

Author

Benoit Cloitre, Mar 08 2002

Extensions

Listed terms verified by Klaus Brockhaus, Sep 04 2009

Status

approved