A068374 Primes p such that positive values of p - A002110(k) are all primes for k > 0.

2, 5, 13, 19, 43, 73, 103, 109, 229, 313, 883, 1093, 1489, 1699, 1789, 2143, 3463, 3853, 5653, 15649, 21523, 43789, 47743, 50053, 51199, 59473, 86293, 88819, 93493, 101533, 176053, 197299, 205663, 235009, 257503, 296509, 325543, 338413, 347989

Offset: 1

Author

Naohiro Nomoto, Mar 01 2002

Keywords

• easy
• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..121

Crossrefs

Cf. A002110.

Programs

MATLAB

Primes = primes(10^8);
A = Primes;
primorial = 1;
for k =1:10
  primorial = primorial*Primes(k);
j = find(A > primorial,1,'first');
  if numel(j) == 0
    break
  end
  A = [A(1:j-1),intersect(A(j:end),Primes + primorial)];
end
A % Robert Israel, Dec 14 2015

Maple

primo:= proc(k) option remember; ithprime(k)*procname(k-1) end proc:
primo(1):= 2:
filter:= proc(p)
  local k;
  if not isprime(p) then return false fi;
  for k from 1 do
    if primo(k) >= p then return true
    elif not isprime(p - primo(k)) then return false
    fi
  od
end proc:
select(filter, [2,seq(i,i=3..10^6,2)]); # Robert Israel, Dec 14 2015

Mathematica

s = Table[Product[Prime@ k, {k, n}], {n, 12}]; Select[Prime@ Range@ 30000, AllTrue[# - TakeWhile[s, Function[k, k < #]], PrimeQ@ # && # > 0 &] &] (* Michael De Vlieger, Dec 14 2015, Version 10 *)

PARI

primo(n) = prod(k=1, n, prime(k));
isok(p) = {my(k=1); while ((pp=primo(k)) < p, if (! isprime(p-pp), return (0)); k++;); return (1);}
lista(nn) = forprime(p=2, nn, if (isok(p), print1(p, ", "));); \\ Michel Marcus, Dec 14 2015