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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
OFFSET
1,1
COMMENTS
The original definition ("Primes p such that the minimum value of |p-2^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, ..., .
EXAMPLE
a(1)=5 since 5 is the third prime number and 2^3-5 = 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
Benoit Cloitre, Dec 17 2002
EXTENSIONS
Edited (corrected title) and extended by Robert G. Wilson v, Jul 06 2014
STATUS
approved