A225236 Primes a(n) = 1 + p_1 + p_1*p_2 + p_1*p_2*p_3 + ... + p_1*p_2*...*p_n where p_1 < p_2 < ... < p_n are the smallest possible primes, with p_1 = 2.

3, 13, 83, 853, 32423, 3599833, 535143923, 89303006953, 15446143311143, 3962154101487973, 1112987090349177203, 352673891880866663113, 151875423856593903090323, 74549545656530694788850433, 62494194870870101337941582723, 53556130238578900142519833155253

Offset

1,1

Comments

a(n) = 1 + sum of product of primes p_i from i = 1 to n such that p_i < p_(i+1) and a(n) is prime.

The corresponding primes p_i are:

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,...

a(n) ==3 (mod 10) because p_1*p_2*...*p_n == 0 (mod 10).

Property of this sequence:

b(n) = (a(n) - 1)/2 = 6, 41, 426, 16211, 1799916,... is alternatively even == 6 mod 10 and odd == 1 mod 10.

An easy way to write and compute these numbers is the nested product 1 + p_1*(1 + p_2*(1 + p_3*...))). - T. D. Noe, May 03 2013

Links

Table of n, a(n) for n=1..16.

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 1000 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, `, ppp):else fi:od:od:

Crossrefs

Cf. A006862, A143293.

Sequence in context: A123114 A104032 A130406 * A152789 A192943 A366657

Adjacent sequences: A225233 A225234 A225235 * A225237 A225238 A225239

Keyword

nonn

Author

Michel Lagneau, May 03 2013

Status

approved