A369272 - OEIS

%I #9 Jan 24 2024 08:24:40

%S 1,3,2,6,7,5,4,9,8,12,10,14,15,11,16,18,20,21,22,24,25,27,26,30,28,33,

%T 32,36,35,44,39,40,42,45,34,50,48,55,38,51,46,60,49,54,56,57,52,65,58,

%U 63,62,66,70,77,64,69,68,72,75,84,80,78,85,81,74,90,91,87,76,93,82,95,86,96,98,99

%N a(1) = 1; for n > 1, a(n) is the smallest positive number that has not yet appeared that is a multiple of the smallest prime that does not divide n*a(n-1).

%C The sequence is conjectured to be a permutation of the positive integers, although it takes many terms for the primes to appear, e.g., a(63784) = 23.

%H Scott R. Shannon, <a href="/A369272/b369272.txt">Table of n, a(n) for n = 1..10000</a>

%H Scott R. Shannon, <a href="/A369272/a369272.png">Image of the first 100000 terms</a>. The green line is a(n) = n.

%e a(7) = 4 as 2 is the smallest prime that does not divide a(6)*7 = 5*7 = 35, and 4 = 2*2 is the smallest multiple of 2 that has not yet appeared.

%Y Cf. A369271, A351495, A053669.

%K nonn

%O 1,2

%A _Scott R. Shannon_, Jan 18 2024