A263267 Breadth-first traversal of the tree defined by the edge-relation A049820(child) = parent.
0, 1, 2, 3, 4, 6, 5, 8, 9, 10, 12, 7, 11, 14, 18, 13, 15, 16, 20, 22, 17, 24, 25, 26, 28, 30, 19, 21, 32, 34, 23, 40, 38, 42, 27, 44, 48, 46, 29, 36, 50, 56, 60, 49, 52, 54, 31, 33, 72, 58, 35, 84, 62, 66, 37, 39, 96, 68, 70, 41, 45, 104, 108, 74, 76, 78, 80, 43, 47, 120, 81, 82, 90, 88, 51, 128, 132, 83, 85, 86, 94, 53, 55, 136, 140, 87, 92, 102
Offset: 0
Examples
Rows 0 - 21 of the table. The lines show the nodes of the tree connected by the edge-relation A049820(child) = parent:
0;
| \
1, 2;
| \ \
3, 4, 6;____
| | | \ \
5, 8, 9, 10, 12;
| | | |
7, _ 11, 14, 18;
/ | \ \ \
13, 15, 16, 20, 22;____
| | / | \ \
17, 24, 25, 26, 28, 30;
| \ | |
19, 21, 32, 34;
| | | \
23, 40, 38, 42;____
| | \ \
27, 44, 48, 46;____
| \ | | \ | \ \
29, 36, 50, 56, 60, 49, 52, 54;
| \ | |
31, 33, 72, 58;
| | | \
35, 84, 62, 66;
| \ | | \
37, 39, 96, 68, 70;_______
| \ | \ / | \ \
41, 45, 104, 108, 74, 76, 78, 80;
| | | | | \ \
43, 47, 120, _81, 82, 90, 88;
| | \ / | | |
51, 128, 132, 83, 85, 86, 94;
| \ | \ | | |
53, 55 136, 140 87, 92, 102;______
| | \ | | \ \
57,_ 89, 91, 98, 106, 110, 112;
/ | \ / / \ | |
59, 63, 64, 93, 95, 100, 114, 116;
| | | | \
61, 99, 97, _118, 126;
| | | / | \
65, 101, 105, 121, 122, 124;
(See also _Michael De Vlieger_'s poster in the Links section.)
Links
Crossrefs
Inverse permutation: A263268.
Cf. A264988 (the left edge), this differs from A261089 (the least term on each level) for the first time at level 69.
Cf. A263269 (the right edge).
Cf. A262686 (maximum term on the level n).
Cf. A045765 (the leaves of the tree).
Cf. also permutations A263265 (obtained from this table by sorting each row into ascending order), A263266.
Cf. also A088975.
Programs
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PARI
uplim = 125753; \\ = A263260(10001). checklimit = 1440; \\ Hard limit 1440 good for at least up to A002182(67) = 1102701600 as A002183(67) = 1440. v263267 = vector(uplim); A263267 = n -> if(!n,n,v263267[n]); z = 0; for(n=0, uplim, t = A263267(n); write("b263267.txt", n, " ", t); for(k=t+1, t+checklimit, if((k-numdiv(k)) == t, z++; if(z <= uplim, v263267[z] = k))));
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Sage
# After David Eppstein's Python-code for A088975. def A263267(): '''Breadth-first reading of irregular tree defined by the edge-relation A049820(child) = parent''' yield 0 for x in A263267(): for k in [x+1 .. 2*(x+1)]: if ((k - sloane.A000005(k)) == x): yield k def take(n,g): '''Returns a list composed of the next n elements returned by generator g.''' return [next(g) for _ in range(n)] take(120, A263267())
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Scheme
;; This version creates the list of terms incrementally, using append! function that physically modifies the list at the same time as it is traversed. Otherwise the idea is essentially the same as with Python/Sage-program above: (define (A263267list_up_to_n_terms_at_least n) (let ((terms-produced (list 0))) (let loop ((startp terms-produced) (endp terms-produced) (k (- n 1))) (cond ((<= k 0) terms-produced) (else (let ((children (children-of-n-in-A049820-tree (car startp)))) (cond ((null? children) (loop (cdr startp) endp k)) (else (begin (append! endp children) (loop (cdr startp) children (- k (length children)))))))))))) (define (children-of-n-in-A049820-tree n) (let loop ((k (A262686 n)) (children (list))) (cond ((<= k n) children) ((= (A049820 k) n) (loop (- k 1) (cons k children))) (else (loop (- k 1) children)))))
Comments