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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 5 02:46 EDT 2023. Contains 363130 sequences. (Running on oeis4.)