login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) is the smallest divisor of the n-th nonprime number (A018252(n)) not already in the sequence.
1

%I #11 Jul 29 2019 17:01:18

%S 1,2,3,4,9,5,6,7,15,8,18,10,21,11,12,25,13,27,14,30,16,33,17,35,36,19,

%T 39,20,42,22,45,23,24,49,50,51,26,54,55,28,57,29,60,31,63,32,65,66,34,

%U 69,70,72,37,75,38,77,78,40,81,41,84,85,43,87,44,90,91

%N a(n) is the smallest divisor of the n-th nonprime number (A018252(n)) not already in the sequence.

%C This sequence is a permutation of the natural numbers.

%C Empirically:

%C - the subsequence with the terms satisfying a(n) <= n correspond to A093641,

%C - if a(n) > n, then a(n) = A018252(n),

%C - these two situations appear as two lines in the scatterplot of the sequence.

%H Rémy Sigrist, <a href="/A326776/b326776.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A326776/a326776.gp.txt">PARI program for A326776</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e The first terms, alongside the divisors of A018252(n), are:

%e n a(n) div(A018252(n))

%e -- ---- ---------------

%e 1 1 (1)

%e 2 2 (1, 2, 4)

%e 3 3 (1, 2, 3, 6)

%e 4 4 (1, 2, 4, 8)

%e 5 9 (1, 3, 9)

%e 6 5 (1, 2, 5, 10)

%e 7 6 (1, 2, 3, 4, 6, 12)

%e 8 7 (1, 2, 7, 14)

%e 9 15 (1, 3, 5, 15)

%e 10 8 (1, 2, 4, 8, 16)

%o (PARI) See Links section.

%Y Cf. A018252, A093641, A111273.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jul 28 2019