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A068394
Numbers k such that the k-th digit of Pi and the k-th digit of e are the same.
5
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
KEYWORD
easy,nonn,base
AUTHOR
Benoit Cloitre, Mar 08 2002
EXTENSIONS
Listed terms verified by Klaus Brockhaus, Sep 04 2009
STATUS
approved