OFFSET
1,2
COMMENTS
Let p_i denote the i-th prime. If the prime decompositions of x and y are
x = Product_{i=1..5} p_i^e_i*q_x, y = Product_{i=1..5} p_i^f_i*q_y,
then we define gcd_11(x, y) to be Product_{i=1..5} p_i^min{e_i, f_i}.
The sequence is the lexicographically earliest infinite sequence {a(n)} of distinct positive numbers such that, for n>2, gcd_11(a(n), a(n-1)) > 1 and gcd_11(a(n), a(n-2)) = 1.
An analog of A336957, but using only the first five primes.
Frank Stevenson has proved that a(n) always exists, something that is not true if only the primes 2, 3, 5, 7 are used. He remarks that because the small primes 13, 17, 19, ... cannot be used in the construction, some numbers take a long time to appear - are very late, in the terminology of A338053.
As can be seen from the graph, this is a much more irregular sequence than A336957.
LINKS
Frank Stevenson, Table of n, a(n) for n = 1..843
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 11 2020, based on an email from Frank Stevenson, Aug 26 2020
STATUS
approved