A227613 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).

2, 5, 7, 11, 41, 113, 149, 167, 173, 257, 281, 317, 431, 491, 839, 857, 953, 977, 1031, 1091, 2909, 3041, 3191, 3467, 4073, 4721, 5381, 6047, 6791, 7127, 8243, 8387, 9743, 10709, 11831, 12011, 12119, 13163, 14249, 14633, 17891, 22157, 22397, 23789, 24419, 25469

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..46.

Example

a(1) = 2 because 1 + a(1) = 3 = A225236(1);
a(2) = 5 because 1 + a(1) + a(1)*a(2) = 1 + 2 + 2*5 = 13 = A225236(2);
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).

Maple

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:

Crossrefs

Cf. A225236.

Sequence in context: A131102 A235468 A229209 * A168031 A260108 A265791

Adjacent sequences: A227610 A227611 A227612 * A227614 A227615 A227616

Keyword

nonn

Author

Michel Lagneau, Jul 19 2013

Status

approved