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A126917
a(1)=1. a(n) = the (largest proper divisor of n)th integer from among those positive integers not occurring earlier in the sequence.
8
1, 2, 3, 5, 4, 8, 6, 11, 10, 14, 7, 17, 9, 20, 18, 23, 12, 26, 13, 29, 25, 32, 15, 35, 24, 38, 33, 41, 16, 44, 19, 47, 40, 50, 34, 53, 21, 56, 48, 59, 22, 62, 27, 65, 55, 68, 28, 71, 43, 74, 63, 77, 30, 80, 54, 83, 70, 86, 31, 89, 36, 92, 78, 95, 64, 98, 37, 101, 85, 104, 39
OFFSET
1,2
COMMENTS
Sequence is a permutation of the positive integers.
EXAMPLE
The largest proper divisor of 8 is 4. So a(8) is the 4th integer from among those not occurring among the first 7 integers of the sequence (a(8) is the 4th integer from among 7,9,10,11,13,14,..). So a(8) = 11.
MATHEMATICA
f[l_List] := Block[{k = 0, c = Divisors[Length[l] + 1][[ -2]]}, While[c > 0, k++; While[MemberQ[l, k], k++ ]; c--; ]; Append[l, k]]; Nest[f, {1}, 71] (* Ray Chandler, Jan 04 2007 *)
PROG
(Scheme, with defineperm1-macro from Antti Karttunen's IntSeq-library)
(defineperm1 (A126917 n) (if (<= n 1) n (let loop ((i (A243069 (- n 1))) (the-n-th-one (- (A032742 n) 1))) (cond ((not-lte? (A126918 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 b) also in case a is nil.
;; (Because of the stateful caching system used by defineperm1-macro):
(define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))
;; Antti Karttunen, Jun 20 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 31 2006
EXTENSIONS
Extended by Ray Chandler, Jan 04 2007
STATUS
approved