This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078686 #37 May 29 2025 17:40:46
%S A078686 5,31,67,89,101,283,503,1039,1129,2069,3457,5641,45763,71483,86599,
%T A078686 112921,161411,210173,211007,232741,245269,479029,1078589
%N A078686 Primes prime(k) such that 2^k - prime(k) is also prime.
%C A078686 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.
%C A078686 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, ..., .
%e A078686 a(1)=5 since 5 is the third prime number and 2^3-5 = 3 is prime. - _Robert G. Wilson v_, Jul 06 2014
%t A078686 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 *)
%t A078686 Select[Table[{n,Prime[n]},{n,40000}],PrimeQ[2^#[[1]]-#[[2]]]&][[All,2]] (* _Harvey P. Dale_, Feb 19 2020 *)
%Y A078686 Corresponding k are in A078583.
%Y A078686 Cf. A000040, A242944, A188677.
%K A078686 nonn,more
%O A078686 1,1
%A A078686 _Benoit Cloitre_, Dec 17 2002
%E A078686 Edited (corrected title) and extended by _Robert G. Wilson v_, Jul 06 2014
%E A078686 a(23) from _Michael S. Branicky_, May 29 2025