A338055 - OEIS

%I #30 Jan 03 2021 01:43:46

%S 1,2,6,15,35,14,12,33,55,10,18,21,77,22,20,45,63,28,40,75,99,44,50,

%T 105,231,88,80,135,147,56,100,165,189,98,110,225,441,112,160,275,297,

%U 24,70,385,363,36,140,539,891,30,175,847,66,60,245,3773,132,90,875,5929,176,48

%N Lexicographically earliest infinite sequence {a(n)} of distinct positive numbers such that, for n>2, a(n) has a common factor with a(n-1) involving only primes <= 11 but no such common factor with a(n-2) (primes > 11 play no role in this definition).

%C Let p_i denote the i-th prime. If the prime decompositions of x and y are

%C    x = Product_{i=1..5} p_i^e_i*q_x, y = Product_{i=1..5} p_i^f_i*q_y,

%C then we define gcd_11(x, y) to be Product_{i=1..5} p_i^min{e_i, f_i}.

%C 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.

%C An analog of A336957, but using only the first five primes.

%C 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.

%C As can be seen from the graph, this is a much more irregular sequence than A336957.

%H Frank Stevenson, <a href="/A338055/b338055.txt">Table of n, a(n) for n = 1..843</a>

%Y Cf. A336957, A338053, A338054.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Oct 11 2020, based on an email from Frank Stevenson, Aug 26 2020