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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified February 24 10:37 EST 2020. Contains 332209 sequences. (Running on oeis4.)