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

%I A068374 #26 Feb 16 2021 00:59:40
%S A068374 2,5,13,19,43,73,103,109,229,313,883,1093,1489,1699,1789,2143,3463,
%T A068374 3853,5653,15649,21523,43789,47743,50053,51199,59473,86293,88819,
%U A068374 93493,101533,176053,197299,205663,235009,257503,296509,325543,338413,347989
%N A068374 Primes p such that positive values of p - A002110(k) are all primes for k > 0.
%H A068374 Robert Israel, <a href="/A068374/b068374.txt">Table of n, a(n) for n = 1..121</a>
%p A068374 primo:= proc(k) option remember; ithprime(k)*procname(k-1) end proc:
%p A068374 primo(1):= 2:
%p A068374 filter:= proc(p)
%p A068374   local k;
%p A068374   if not isprime(p) then return false fi;
%p A068374   for k from 1 do
%p A068374     if primo(k) >= p then return true
%p A068374     elif not isprime(p - primo(k)) then return false
%p A068374     fi
%p A068374   od
%p A068374 end proc:
%p A068374 select(filter, [2,seq(i,i=3..10^6,2)]); # _Robert Israel_, Dec 14 2015
%t A068374 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 *)
%o A068374 (PARI) primo(n) = prod(k=1, n, prime(k));
%o A068374 isok(p) = {my(k=1); while ((pp=primo(k)) < p, if (! isprime(p-pp), return (0)); k++;); return (1);}
%o A068374 lista(nn) = forprime(p=2, nn, if (isok(p), print1(p, ", "));); \\ _Michel Marcus_, Dec 14 2015
%o A068374 (MATLAB)
%o A068374 Primes = primes(10^8);
%o A068374 A = Primes;
%o A068374 primorial = 1;
%o A068374 for k =1:10
%o A068374   primorial = primorial*Primes(k);
%o A068374 j = find(A > primorial,1,'first');
%o A068374   if numel(j) == 0
%o A068374     break
%o A068374   end
%o A068374   A = [A(1:j-1),intersect(A(j:end),Primes + primorial)];
%o A068374 end
%o A068374 A % _Robert Israel_, Dec 14 2015
%Y A068374 Cf. A002110.
%K A068374 easy,nonn
%O A068374 1,1
%A A068374 _Naohiro Nomoto_, Mar 01 2002