

A209296


Primes obtained from recursively adding to a 0th term of 1 the product of the first k (current number of addends) primes not dividing the predecessor.


1




OFFSET

1,1


COMMENTS

An unsubmitted supersequence with an initial term of value 1 and index 0 is implicitly referenced. Term k+1 in this supersequence results by adding to its kth term the product of the smallest k primes not dividing it. Thus, each term in the sequence results by adding either the kth primorial or the prior primorial times some prime larger than the kth prime. To a point beyond the possibility of evaluating the primality status for the sum, only two early additions are not of primorials; and in both of these cases the next prime after the kth is introduced.
This sequence was partly motivated by considering the search for primorial primes, this being one of the simpler ways of also ensuring nondivisibility by the first so many primes. Other than giving terms in the sum different numbers of prime factors beginning with 0, there is nothing special about starting with 1: A similar sequence may be produced with any integer starting value.
Many strings of 4 or more consecutive digits the same, including six successive 8s, five successive 5s, and two samedigit quadruples very near to each other, were found noteworthy by the author in the terms calculated.
The program below gives [A187750values]:a(n):[Length] and a sentence for the exceptional adds. A187750 holds the supersequence indices for this sequence.


LINKS



EXAMPLE

a(1) = 1 + 2# = 1 + 2 = 3. Because 3 divides this and 1 + 2 + 2*5 = 13 is prime, this is a(2). a(3) = a(2) + 5# = 13 + 30 = 43. The next 3 terms in sum are 7#, 7#*13 (11 divides 43 + 7# = 253) and 13#, with a(4) resulting from the last because the 4th and 5th terms in the unsubmitted supersequence are composite.


PROG

(PARI)
{
n=1; i=1;
while(1,
a=prod(j=1, i1, prime(j)); k=i;
while(n%prime(k)==0, k++; next()); n+=a*prime(k);
if(ispseudoprime(n),
print1(i":"n"::"ceil(log(n)/log(10))"\n"));
if(k!=i,
print1("Term "i+1" of the sum is not a primorial.\n"));
i++;
next())
}


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



