

A249721


Numbers whose base3 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
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OFFSET

0,2


COMMENTS

9 divides neither C(s1,s/2) (= A001700(s/2)) nor C(s,s/2) (= A000984(s/2)) if and only if s = a(n).


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192


FORMULA

a(n) = 2 * A051382(n).


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

(Scheme, with Antti Karttunen's IntSeqlibrary)
(define A249721 (MATCHINGPOS 0 0 in_A249721?))
(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:
(define (A249721 n) (* 2 (A051382 n)))


CROSSREFS

Cf. A007089, A051382, A249719, A249720, A001700, A000984, A117966, A249733.
Sequence in context: A043765 A043569 A273131 * A010063 A260652 A324102
Adjacent sequences: A249718 A249719 A249720 * A249722 A249723 A249724


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Nov 14 2014


STATUS

approved



