A257466 - OEIS

%I #19 May 17 2015 05:37:21

%S 2,17,11,5,3,101,19469,38669,191459,191,59,3877889,494272241,

%T 360772331,6004094833991,41320119600341

%N Smallest prime number p such that p + pps(1), p + pps(2), ..., p + pps(n) are all prime but p + pps(n+1) is not, where pps(n) is the partial primorial sum (A060389(n)).

%C The n-th member in the sequence m is the smallest prime with exactly n prime terms starting from m + 2.

%e For prime 3: 3+2, 3+8, 3+38, 3+248 are all prime. 3+2558 = 13 * 197 is not. So a(4)= 3. (3 is the smallest prime that has exactly 4 terms.)

%e 2 has zero terms because 2+2 is composite, so a(0)=2.

%o (PARI) pps(n)=my(s, P=1); forprime(p=2, prime(n), s+=P*=p); s;

%o isokpps(p, n) = {for (k=1, n, if (!isprime(p+pps(k)), return (0));); if (!isprime(p+pps(n+1)), return (1));}

%o a(n) = {my(p = 2); while (!isokpps(p,n), p = nextprime(p+1)); p;} \\ _Michel Marcus_, May 02 2015

%Y Cf. A060389, A257467.

%K hard,nonn,more

%O 0,1

%A _Fred Schneider_, Apr 25 2015

%E a(15) from _Fred Schneider_, May 15 2015