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A385661 Lexicographically earliest sequence of distinct positive integers that can be partitioned into runs of pairwise coprime integers, the n-th such run having a(n) terms.

%I A385661 #14 Aug 15 2025 09:11:00
%S A385661 1,2,3,4,5,7,6,11,13,17,8,9,19,23,25,10,21,29,31,37,41,43,12,35,47,53,
%T A385661 59,61,14,15,67,71,73,79,83,89,97,101,103,16,27,49,55,107,109,113,127,
%U A385661 131,137,139,149,151,18,65,77,157,163,167,173,179,181,191,193,197,199,211,223,227,229
%N A385661 Lexicographically earliest sequence of distinct positive integers that can be partitioned into runs of pairwise coprime integers, the n-th such run having a(n) terms.
%C A385661 This sequence is a permutation of the positive integers as each run starts with the least integer not yet in the sequence.
%C A385661 The prime numbers appear in natural order.
%H A385661 Rémy Sigrist, <a href="/A385661/b385661.txt">Table of n, a(n) for n = 1..10000</a>
%H A385661 Rémy Sigrist, <a href="/A385661/a385661.gp.txt">PARI program</a>
%H A385661 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A385661 T(n, 1) = 2*n-2 for any n > 1.
%e A385661 The first terms and runs are:
%e A385661   n   a(n)  n-th run
%e A385661   --  ----  -----------------------------------------------------------
%e A385661    0     1  1
%e A385661    1     2  2, 3
%e A385661    3     3  4, 5, 7
%e A385661    6     4  6, 11, 13, 17
%e A385661   10     5  8, 9, 19, 23, 25
%e A385661   15     7  10, 21, 29, 31, 37, 41, 43
%e A385661   22     6  12, 35, 47, 53, 59, 61
%e A385661   28    11  14, 15, 67, 71, 73, 79, 83, 89, 97, 101, 103
%e A385661   39    13  16, 27, 49, 55, 107, 109, 113, 127, 131, 137, 139, 149, 151
%o A385661 (PARI) \\ See Links section.
%Y A385661 See A386932 for a similar sequence.
%Y A385661 Cf. A076034, A385735 (inverse).
%K A385661 nonn,tabf
%O A385661 1,2
%A A385661 _Rémy Sigrist_, Aug 09 2025