|
Search: id:A102049
|
|
|
| A102049 |
|
Indices of primes which are denominators of convergents to e. |
|
+0
3
|
| |
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The prime denominators of convergents to e form A094008 (so A000040(a(n)) = A094008(n)). Their positions in A007677 (denominators of convergents to e) form A094007, so a(n) = A000720(A007677(A094007(n))).
|
|
REFERENCES
|
E. B. Burger, Diophantine Olympics ..., Amer. Math. Monthly, 107 (Nov. 2000), 822-829.
J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly, to appear.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics\.
|
|
FORMULA
|
a(n) = A000720(A094008(n)).
|
|
EXAMPLE
|
a(1) = 2 because the first convergent to e with prime denominator is 8/3, and the index of 3 is 2, i.e., 3 is the 2nd prime.
|
|
CROSSREFS
|
Cf. A000040, A000720, A007677, A094007, A094008.
Sequence in context: A132498 A087314 A099179 this_sequence A058522 A122736 A092458
Adjacent sequences: A102046 A102047 A102048 this_sequence A102050 A102051 A102052
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 27 2004
|
|
|
Search completed in 0.002 seconds
|
