A078686 Primes prime(i) such that 2^i - prime(i) is also prime.

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, ..., .

Links

Table of n, a(n) for n=1..22.

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

Cf. A000040, A242944, A188677.

Sequence in context: A125743 A332788 A333243 * A031908 A139862 A299505

Adjacent sequences: A078683 A078684 A078685 * A078687 A078688 A078689

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