OFFSET
1,2
COMMENTS
Terms at a(2^n) are: 1, 2, 3, 5, 8, 13, 20, 32, 48, 71, 105, 156, 236, 354, 542, 815, 1228, ...
Fixed points begin as: 1, 2, 6, 10, 18, 42, 92, 26372, ...
LINKS
EXAMPLE
By definition, a(1) = 1.
After that, for n = 2, when its prime factorization is shifted once right, results A064989(2) = 1, so we select the 1st of still unused positive natural numbers, which is 2, thus a(2) = 2.
For n = 3 = p_2 (3 is the second prime), when its prime factorization is shifted once right, results A064989(3) = 2 = p_1, so we select 2nd of still unused numbers, which is 4, thus a(3) = 4.
For n = 4, like for all powers of two, the result of right shifting is 1, so we select the smallest still unused number, which is 3, thus a(4) = 3.
For n = 5 = p_3, A064989(5) = 3 = p_2, so we select the 3rd smallest still unused number from [5, 6, 7, 8, ...] which is 7, thus a(5) = 7.
PROG
(Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)
(defineperm1 (A246165 n) (if (<= n 1) n (let loop ((i 1) (the-n-th-one (- (A064989 n) 1))) (cond ((not-lte? (A246166 i) n) (if (zero? the-n-th-one) i (loop (+ i 1) (- the-n-th-one 1)))) (else (loop (+ i 1) the-n-th-one))))))
;; We consider a > b (i.e. not less than or equivalent to b) also in case a is nil.
;; (Which is needed when using the stateful caching system used by defineperm1-macro):
(define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 17 2014
STATUS
approved