%I
%S 2,3,11,107,119657,2513657,8448047,210336167
%N Define u such that u(1) = k and u(n) = u(n1) + (1)^n*(n!) for n > 1. Terms are numbers k for which the number of consecutive values of u(i), starting at u(1) = k, that are primes reaches a new record high.
%e If k = 2, u(1) = 2 is prime, and no lesser number has this property, thus 2 is a term.
%e If k = 11, u(1) = 11, u(2) = 11 + 2! = 13, u(3) = 13  3! = 7 and u(4) = 7 + 4! = 31 are primes, and no lesser number has this property, thus 11 is a term.
%o (PARI)
%o card(k)=my(s=k,c=2,p=1);while(isprime(s),p*=c;s+=if(c%2,p,p);c++);c=2
%o rec(kk=10^9)=my(r=0);forprime(k=1,kk,x=card(k);if(x>r,if(r>0,print1(", "));print1(k);r=x))
%K nonn,more
%O 1,1
%A _JeanMarc Rebert_, Nov 23 2022
