

A078686


Primes prime(i) such that 2^i  prime(i) is also prime.


5



5, 31, 67, 89, 101, 283, 503, 1039, 1129, 2069, 3457, 5641, 45763, 71483, 86599, 112921, 161411, 210173, 211007, 232741, 245269, 479029
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OFFSET

1,1


COMMENTS

The original definition ("Primes p such that the minimum value of p2^x, x>0, is also a prime") produces A188677, not the terms shown here.  N. J. A. Sloane, Apr 01 2011.
The mystery of this definition was solved by Robert G. Wilson v, Jul 06 2014, who also remarks that if instead we ask for odd primes, and therefore the index is one less than that for all primes, the sequence would begin: 11, 13, 17, 19, 23, 37, 61, 233, 257, 1553, 2879, 4919, 6389, 7621, 8081, 35593, 37951, 96263, 206419, ..., . If we count 1 amongst the primes (A008578), then the sequence would begin: 2, 3, 5, 11, 17, 167, 193, 197, 433, 4111, 9173, 42929, 95279, 98897, 139409, 142567, 228617, ..., .


LINKS



EXAMPLE

a(1)=5 since 5 is the third prime number and 2^35 = 3 is prime.  Robert G. Wilson v, Jul 06 2014


MATHEMATICA

p = 2; lst = {}; While[p < 760001, If[ PrimeQ[ 2^PrimePi@ p  p], AppendTo[lst, p]; Print@ p]; p = NextPrime@ p]; lst (* Robert G. Wilson v, Jul 06 2014 *)
Select[Table[{n, Prime[n]}, {n, 40000}], PrimeQ[2^#[[1]]#[[2]]]&][[All, 2]] (* Harvey P. Dale, Feb 19 2020 *)


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



