A227613 - OEIS

%I #17 Sep 15 2017 19:32:59

%S 2,5,7,11,41,113,149,167,173,257,281,317,431,491,839,857,953,977,1031,

%T 1091,2909,3041,3191,3467,4073,4721,5381,6047,6791,7127,8243,8387,

%U 9743,10709,11831,12011,12119,13163,14249,14633,17891,22157,22397,23789,24419,25469

%N Smallest primes a(n) such that 1 + a(1), 1 + a(1) + a(1)*a(2), ..., 1 + a(1) + a(1)*a(2) + ... + a(1)*a(2)*a(3)*...*a(n) are prime numbers with a(1) = 2 and a(i) < a(i+1).

%C The sequence of the primes 1 + sum of product of a(i) from i = 1 to n such that a(i) < a(i+1) is given by A225236.

%e a(1) = 2 because 1 + a(1) = 3 = A225236(1);

%e a(2) = 5 because 1 + a(1) + a(1)*a(2) = 1 + 2 + 2*5 = 13 = A225236(2);

%e a(3) = 7 because 1 + a(1) + a(1)*a(2) + a(1)*a(2)*a(3) = 1 + 2 + 2*5 + 2*5*7 = 83 = A225236(3).

%p with(numtheory) : a1:=3:p0:=3:p1:=2:k0:=2:for n from 1 to 50 do:ii:=0:for k from k0 to 10^6 while(ii=0) do:p:=ithprime(k):pp:=p1*p: ppp:=p0+pp:if type(ppp, prime)=true then p0:=ppp:p1:=pp: k0:=k+1:ii:=1:printf(`%d, `, p):else fi:od:od:

%Y Cf. A225236.

%K nonn

%O 1,1

%A _Michel Lagneau_, Jul 19 2013