A355555 - OEIS

%I #19 Jul 13 2022 07:20:27

%S 2,17,5,7,53,197,848699,2802313,24281267,54927644129,29566753319

%N a(n) is the first prime prime(j) such that prime(j) + prime(k) + prime(k+1) is prime for k = j+1..j+n but not k = j+n+1.

%C a(11) > 2*10^12. - _Iain Fox_, Jul 09 2022

%e a(3) = 7 because 7+11+13 = 31, 7+13+17 = 37 and 7+17+19 = 41 are prime but 7+19+23 = 49 is not.

%p V:= Array(0..8): count:= 0:

%p f:= proc(n) local p,i;

%p        p:= ithprime(n);

%p        for i from 0 do

%p          if not isprime(p+ithprime(n+i+1)+ithprime(n+i+2)) then return i fi

%p        od

%p end proc:

%p for nn from 1 while count < 9 do

%p    v:= f(nn);

%p    if V[v] = 0 then V[v]:= ithprime(nn)   fi;

%p od:

%p convert(V,list);

%o (PARI) a(n) = my(pk, pk1); forprime(pj=2, oo, pk=nextprime(pj+1); for(x=0, n, pk1=nextprime(pk+1); if(!bitxor(x==n, isprime(pj+pk+pk1)), next(2)); pk=pk1); return(pj)) \\ _Iain Fox_, Jul 06 2022

%Y Cf. A000040.

%K nonn,more,hard

%O 0,1

%A _J. M. Bergot_ and _Robert Israel_, Jul 06 2022

%E a(9)-a(10) from _Iain Fox_, Jul 06 2022