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A266117 Lexicographically first injection of positive integers beginning with a(1) such that a(n)*a(n+1) is a term of A265349, i.e., has no multiple occurrences of any nonzero digit when viewed in factorial base (A007623). 6
1, 2, 3, 4, 5, 10, 11, 6, 7, 12, 8, 9, 24, 13, 18, 19, 26, 14, 17, 22, 21, 16, 15, 32, 30, 20, 23, 29, 42, 28, 25, 48, 34, 53, 41, 54, 27, 40, 33, 36, 37, 61, 65, 44, 49, 72, 39, 38, 51, 52, 55, 59, 47, 46, 58, 50, 60, 62, 31, 66, 56, 57, 64, 45, 80, 63, 74, 69, 68, 35, 79, 100, 73, 43, 67, 70, 71, 78, 84, 87, 92, 90, 76, 96, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

After a(1) = 1, always choose for a(n+1) the least unused k such that in factorial base representation (A007623), the product a(n)*a(n+1) will not show any of the nonzero digits present twice (or more times), regardless of the positions of the digits.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..14641

Eric Angelini, a(n)*a(n+1) shows at least twice the same digit, Posting on SeqFan-list Dec 21 2015. [Source of inspiration for this sequence.]

Index entries for sequences related to factorial base representation

Index entries for sequences that are permutations of the natural numbers

EXAMPLE

For n = 6, we start searching from the least not yet used number in range a(1) .. a(5) [which is 6, because all the previous terms are fixed] for the first number whose product with a(5) = 5 results a number in A265349.

Multiplying 5 (in factorial base "21") with 6 (in factorial base "100") results 30, which in factorial base is "1100", containing digit "1" twice, thus 6 is disqualified.

Similarly, products 5*7, 5*8 and 5*9 result 35 = "1121", 40 = "1220" and 45 = "1311", where in all cases one of the nonzero digits occur more than once, so 7, 8 and 9 are also all disqualified.

But 5*10 = 50, which has a factorial base representation ("2010") that matches the criterion, thus a(6) = 10.

PROG

(Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)

;; Reference-implementation, quite sub-optimal:

(defineperm1 (A266117 n) (if (= 1 n) n (let ((prev (A266117 (- n 1)))) (let loop ((k 1)) (cond ((and (not-lte? (A266118 k) (- n 1)) (= (A264990 (* k prev)) 1)) k) (else (loop (+ 1 k))))))))

;; We consider a > b (i.e. not less than b) also in case a is #f.

;; (Because of the stateful caching system used by defineperm1-macro):

(define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))

CROSSREFS

Left inverse: A266118 (also the right inverse if this sequence is a permutation of the positive integers).

Cf. A264990, A265349.

Cf. also A266121, A266191 and A266195 for similar permutations.

Sequence in context: A338749 A072701 A261039 * A037473 A007092 A241213

Adjacent sequences:  A266114 A266115 A266116 * A266118 A266119 A266120

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Dec 22 2015

STATUS

approved

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Last modified September 19 00:22 EDT 2021. Contains 347549 sequences. (Running on oeis4.)