|
|
A107899
|
|
Numbers k such that the sum of the terms of the continued fraction for prime(k)/k is prime.
|
|
5
|
|
|
1, 2, 4, 5, 7, 8, 13, 14, 16, 17, 20, 22, 23, 24, 31, 32, 37, 41, 44, 47, 49, 50, 63, 68, 69, 71, 73, 78, 81, 82, 84, 86, 89, 93, 98, 101, 109, 111, 119, 121, 126, 130, 131, 132, 135, 138, 142, 143, 145, 150, 164, 169, 175, 176, 189, 190, 197, 201, 202, 205, 211, 214
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Indices of primes occurring in A107900.
|
|
LINKS
|
|
|
EXAMPLE
|
17 is in this sequence because the 17th prime is 59, 59/17 = 3 + 1/(2 + 1/8), the terms of the continued fraction are {3, 2, 8), and the sum of the terms is the prime number 13.
|
|
MAPLE
|
filter:= n -> isprime(convert(Term(NumberTheory:-ContinuedFraction(ithprime(n)/n), all), `+`)):
|
|
MATHEMATICA
|
s={}; Do[If[PrimeQ[Plus@@ContinuedFraction[Prime[n]/n]], s=Append[s, n]], {n, 300}]; A107899=s
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|