A188677 -id:A188677 - cp's OEIS frontend

A078686 Primes prime(k) such that 2^k - prime(k) 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, 1078589

Offset: 1

Benoit Cloitre, Dec 17 2002

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, ..., .

			a(1)=5 since 5 is the third prime number and 2^3-5 = 3 is prime. - _Robert G. Wilson v_, Jul 06 2014

Corresponding k are in A078583.

Cf. A000040, A242944, A188677.

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 *)

Edited (corrected title) and extended by Robert G. Wilson v, Jul 06 2014

a(23) from Michael S. Branicky, May 29 2025

cp's OEIS Frontend

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

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