A277905 Irregular table: Each row n (n >= 0) lists in ascending order all A018819(n) numbers k for which A048675(k) = n.

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, 128, 7, 25, 45, 60, 80, 81, 108, 144, 192, 256, 14, 50, 90, 120, 160, 162, 216, 288, 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

Offset

1,2

Comments

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.

Note that although the indexing of rows start from zero, the indexing of this sequence starts from 1, with a(1) = 1.

Links

Antti Karttunen, Table of n, a(n) for n = 1..166

Index entries for sequences that are permutations of the natural numbers

Formula

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.]

Other identities. For all n >= 1:

A048675(a(n)) = A277903(n).

Example

The irregular table begins as:
  row terms
   0   1;
   1   2;
   2   3,  4;
   3   6,  8;
   4   5,  9,  12,  16;
   5  10, 18,  24,  32;
   6  15, 20,  27,  36,  48,  64;
   7  30, 40,  54,  72,  96, 128;
   8   7, 25,  45,  60,  80,  81, 108, 144, 192, 256;
   9  14, 50,  90, 120, 160, 162, 216, 288, 384, 512;
  10  21, 28,  75, 100, 135, 180, 240, 243, 320, 324, 432,  576,  768, 1024;
  11  42, 56, 150, 200, 270, 360, 480, 486, 640, 648, 864, 1152, 1536, 2048;
...

Prog

(Scheme)
(definec (A277905 n) (A277905bi (A277903 n) (A277904 n)))
(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.
;; Implementation based on a naive recurrence:
(definec (A277905 n) (if (= 1 n) n (let ((maybe_next (A277896 (A277905 (- n 1))))) (if (not (zero? maybe_next)) maybe_next (A019565 (A277903 n))))))

Crossrefs

Cf. A019565 (the left edge, the only terms that are squarefree).

Cf. A000079 (the trailing edge).

Cf. A048675, A260443, A277886, A277896, A277903, A277904.

Sequence in context: A245704 A260425 A352064 * A257802 A369271 A225850

Adjacent sequences: A277902 A277903 A277904 * A277906 A277907 A277908

Keyword

nonn,tabf

Author

Antti Karttunen, Nov 14 2016

Status

approved