A270884 Smallest of 4 consecutive prime numbers that when represented as a simple continued fraction, generates prime numbers in the numerator and denominator, when reduced.

41, 367, 619, 659, 701, 2267, 2789, 3253, 3463, 6917, 8969, 9221, 11959, 13499, 14431, 17359, 17851, 20143, 22283, 23669, 26107, 27847, 28547, 28879, 29537, 32503, 32717, 32987, 37549, 40709, 40849, 41647, 45971

Offset

1,1

Comments

Order in which the simple continued fraction generated is important. In this case increasing order.

Links

Abhiram R Devesh, Table of n, a(n) for n = 1..100

Example

for a = 41, the set is [41, 43, 47, 53] in simple continued fraction is
41 +       1
     ----------------
       43  +    1
            ---------
             47 + 1
                 ----
                  53
When reduced 4398061/107209; where 4398061 and 107209 are both primes.

Mathematica

Select[Prime@ Range[10^4], AllTrue[{Numerator@ #, Denominator@ #} &@ FromContinuedFraction@ Prime@ Range[#, # + 3] &@ PrimePi@ #, PrimeQ] &] (* Michael De Vlieger, Apr 02 2016, Version 10 *)
cfpnQ[lst_]:=Module[{fcf=FromContinuedFraction[lst]}, AllTrue[{Numerator[ fcf], Denominator[ fcf]}, PrimeQ]]; Select[Partition[Prime[ Range[ 5000]], 4, 1], cfpnQ][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 06 2020 *)

Crossrefs

Sequence in context: A196644 A196599 A142571 * A189438 A297586 A196576

Adjacent sequences: A270881 A270882 A270883 * A270885 A270886 A270887

Keyword

hard,nonn

Author

Abhiram R Devesh, Mar 25 2016

Status

approved