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A377093 Irregular table read by rows; for any n > 0, let u(n) be the least positive integer not among the first n-1 rows; the n-th row lists the u(n) least multiples of u(n) not yet in the sequence.

%I A377093 #9 Oct 19 2024 08:35:58
%S A377093 1,2,4,3,6,9,5,10,15,20,25,7,14,21,28,35,42,49,8,16,24,32,40,48,56,64,
%T A377093 11,22,33,44,55,66,77,88,99,110,121,12,36,60,72,84,96,108,120,132,144,
%U A377093 156,168,13,26,39,52,65,78,91,104,117,130,143,169,182
%N A377093 Irregular table read by rows; for any n > 0, let u(n) be the least positive integer not among the first n-1 rows; the n-th row lists the u(n) least multiples of u(n) not yet in the sequence.
%C A377093 This sequence combines features of Golomb's sequence (A001462) and A361748.
%C A377093 This sequence is a permutation of the positive integers with inverse A377094.
%H A377093 Rémy Sigrist, <a href="/A377093/b377093.txt">Table of n, a(n) for n = 1..10258</a>
%H A377093 Rémy Sigrist, <a href="/A377093/a377093.gp.txt">PARI program</a>
%H A377093 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A377093 The first rows are:
%e A377093     1;
%e A377093     2, 4;
%e A377093     3, 6, 9;
%e A377093     5, 10, 15, 20, 25;
%e A377093     7, 14, 21, 28, 35, 42, 49;
%e A377093     8, 16, 24, 32, 40, 48, 56, 64;
%e A377093     11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121;
%e A377093     12, 36, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168;
%e A377093     ...
%o A377093 (PARI) \\ See Links section.
%o A377093 (Python)
%o A377093 from itertools import count, islice
%o A377093 def A377093gen(): # generator of terms
%o A377093     aset, alst, m = {1, 2, 4}, [1, 2, 4], 3
%o A377093     yield from [1, 2, 4]
%o A377093     for n in count(3):
%o A377093         nlst = []
%o A377093         for k in count(m, m):
%o A377093             if k not in aset:
%o A377093                 nlst.append(k)
%o A377093                 if len(nlst) == m:
%o A377093                     break
%o A377093         yield from nlst
%o A377093         alst.extend(nlst)
%o A377093         aset.update(nlst)
%o A377093         while m in aset: m += 1
%o A377093 print(list(islice(A377093gen(), 70))) # _Michael S. Branicky_, Oct 16 2024
%Y A377093 Cf. A001462, A361748, A376903, A376905, A377094 (inverse).
%K A377093 nonn,tabf
%O A377093 1,2
%A A377093 _Rémy Sigrist_, Oct 16 2024