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%I #23 Nov 21 2016 22:45:26
%S 1,2,3,4,6,8,5,9,12,16,10,18,24,32,15,20,27,36,48,64,30,40,54,72,96,
%T 128,7,25,45,60,80,81,108,144,192,256,14,50,90,120,160,162,216,288,
%U 384,512,21,28,75,100,135,180,240,243,320,324,432,576,768,1024,42,56,150,200,270,360,480,486,640,648,864,1152,1536,2048,35,63,84,112,125,225,300,400
%N Irregular table: Each row n (n >= 0) lists in ascending order all A018819(n) numbers k for which A048675(k) = n.
%C Each row beginning with an odd number (rows with even index) is followed by a row of the same length, with the same terms, but multiplied by 2. See also comments in the Formula section of A018819.
%C Note that although the indexing of rows start from zero, the indexing of this sequence starts from 1, with a(1) = 1.
%H Antti Karttunen, <a href="/A277905/b277905.txt">Table of n, a(n) for n = 1..166</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1; for n > 1, if A277896(a(n-1)) > 0, then a(n) = A277896(a(n-1)), otherwise a(n) = A019565(A277903(n)). [A naive recurrence for a one-dimensional version.]
%F Other identities. For all n >= 1:
%F A048675(a(n)) = A277903(n).
%e The irregular table begins as:
%e row terms
%e 0 1;
%e 1 2;
%e 2 3, 4;
%e 3 6, 8;
%e 4 5, 9, 12, 16;
%e 5 10, 18, 24, 32;
%e 6 15, 20, 27, 36, 48, 64;
%e 7 30, 40, 54, 72, 96, 128;
%e 8 7, 25, 45, 60, 80, 81, 108, 144, 192, 256;
%e 9 14, 50, 90, 120, 160, 162, 216, 288, 384, 512;
%e 10 21, 28, 75, 100, 135, 180, 240, 243, 320, 324, 432, 576, 768, 1024;
%e 11 42, 56, 150, 200, 270, 360, 480, 486, 640, 648, 864, 1152, 1536, 2048;
%e ...
%o (Scheme)
%o (definec (A277905 n) (A277905bi (A277903 n) (A277904 n)))
%o (define (A277905bi row col) (let outloop ((k (A019565 row)) (col col)) (if (zero? col) k (let inloop ((j (+ 1 k))) (if (= (A048675 j) row) (outloop j (- col 1)) (inloop (+ 1 j))))))) ;; Very slow implementation.
%o ;; Implementation based on a naive recurrence:
%o (definec (A277905 n) (if (= 1 n) n (let ((maybe_next (A277896 (A277905 (- n 1))))) (if (not (zero? maybe_next)) maybe_next (A019565 (A277903 n))))))
%Y Cf. A019565 (the left edge, the only terms that are squarefree).
%Y Cf. A000079 (the trailing edge).
%Y Cf. A048675, A260443, A277886, A277896, A277903, A277904.
%K nonn,tabf
%O 1,2
%A _Antti Karttunen_, Nov 14 2016
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