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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
OFFSET
1,2
COMMENTS
Indices of primes occurring in A107900.
LINKS
Eric Weisstein's World of Mathematics, Continued Fraction.
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), `+`)):
select(filter, [$1..300]); # Robert Israel, Jan 08 2024
MATHEMATICA
s={}; Do[If[PrimeQ[Plus@@ContinuedFraction[Prime[n]/n]], s=Append[s, n]], {n, 300}]; A107899=s
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, May 26 2005
STATUS
approved