OFFSET
1,1
COMMENTS
Conjecture: All terms in this sequence (except a(4) = 58 and a(9) = 586) are primes.
FORMULA
a(n) = A013646(prime(n)).
EXAMPLE
a(5) = 61 because 61 is the least integer k whose period of the continued fraction for sqrt(k) is prime(5)=11, namely {1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14}.
MATHEMATICA
n=30; prm={}; fin={}; k=2; While[Length@prm<n||Sort[PrimePi@prm][[;; n]]!=Range@n, If[!IntegerQ@Sqrt@k, l=Length@Last@ContinuedFraction@Sqrt@k, k++]; If[PrimeQ@l, If[FreeQ[prm, l], AppendTo[fin, {k, PrimePi@l}]; AppendTo[prm, l]]]; k++]; First/@SortBy[fin, Last][[;; n]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Giorgos Kalogeropoulos, Jan 04 2022
STATUS
approved