[seqfan] A073674.

Ed Jeffery lejeffery2 at gmail.com
Tue Dec 18 07:20:02 CET 2012

Consider "the" lexicographically smallest permutation of the even natural
numbers such that each partial product with 1 added to it is equal to a
prime. Then the sequence could begin as

2, 6, 8, 28, 4, 26, 10, ...,

with the corresponding primes being

3, 13, 97, 2689, 10753, 279553, 2795521....

Neither sequence is in OEIS (nor is {1, 3, 4, 14, 2, 13, 5,...}).

But, given the rate of growth (seems to be > 2^n*n!) of this sequence of
primes (each k-th partial product is essentially a product of k distinct
natural numbers multiplied by 2^k), how could such an assertion be proved,
since we soon run out of computable or known primes where factorization is
then, well, a factor?

This leads me to the same question regarding A073674. I have searched for a
proof of this sequence but cannot find one. So is there a proof somewhere?


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