|
| |
|
|
A249721
|
|
Numbers whose base-3 representation consists entirely of 0's and 2's, except possibly for a single pair of adjacent 1's among them.
|
|
4
|
|
|
|
0, 2, 4, 6, 8, 12, 14, 18, 20, 22, 24, 26, 36, 38, 42, 44, 54, 56, 58, 60, 62, 66, 68, 72, 74, 76, 78, 80, 108, 110, 114, 116, 126, 128, 132, 134, 162, 164, 166, 168, 170, 174, 176, 180, 182, 184, 186, 188, 198, 200, 204, 206, 216, 218, 220, 222, 224, 228, 230, 234, 236, 238, 240, 242, 324
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
9 divides neither C(s-1,s/2) (= A001700(s/2)) nor C(s,s/2) (= A000984(s/2)) if and only if s = a(n).
|
|
|
LINKS
|
|
|
|
FORMULA
|
|
|
|
EXAMPLE
|
2, which in base 3 is also '2', satisfies the condition, thus it is included;
4, which in base 3 is '11', is included;
6, which in base 3 is '20', is included;
8, which in base 3 is '22', is included;
12, which in base 3 is '110', is included;
14, which in base 3 is '112', is included;
however, e.g., 13, 40, and 130, whose ternary representations are '111', '1111' and '11211' respectively, are not included, because they all contain more than one pair of 1's.
|
|
|
PROG
|
(define (in_A249721? n) (let loop ((n n) (seen11yet? #f)) (cond ((zero? n) #t) ((= 2 n) #t) ((modulo n 3) => (lambda (r) (let ((next_n (/ (- n r) 3))) (cond ((= r 1) (if (or seen11yet? (not (= 1 (modulo next_n 3)))) #f (loop (/ (- next_n 1) 3) #t))) (else (loop next_n seen11yet?)))))))))
;; Or alternatively, based on code for A051382:
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
