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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

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 IntSeq-library)

(define A249721 (MATCHING-POS 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

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)