OFFSET

1,1

COMMENTS

Primes p such that p - A084558(p) is also a prime.

Inspired by the fact that this sequence has a nonempty intersection with A124598.

Let H be the intersection of this sequence and A124598. With some observed exceptions q = 3, 103, 1013, 1223, 2903, ..., if some p in this sequence is in H then the corresponding q also belongs to H. It is unknown whether H is finite.

Based upon the first terms of this sequence, it looks like those k satisfying the definition given in NAME are the even terms of A084558 repeated in certain weakly increasing sequence.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

MAPLE

k:= 0: f:= 1: p:= 1: Res:= NULL: count:= 0:

while count < 100 do

p:= nextprime(p);

while p > f do k:= k+1; f:= f*(k+1) od;

if isprime(p-k) then Res:= Res, p; count:= count+1 fi;

od:

Res; # Robert Israel, Jun 10 2018

MATHEMATICA

Select[Prime@ Range[2^8], PrimeQ[# - Block[{k = 1}, While[k! <= #, k++]; k - 1]] &] (* Michael De Vlieger, Apr 10 2018 *)

PROG

CROSSREFS

KEYWORD

nonn,look

AUTHOR

R. J. Cano, Apr 08 2018

STATUS

approved