A243069 a(n) = smallest natural number that has not yet occurred among the first n terms of A126917.

2, 3, 4, 4, 6, 6, 7, 7, 7, 7, 9, 9, 12, 12, 12, 12, 13, 13, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 19, 19, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 27, 27, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 36, 36, 37, 37, 37, 37, 37, 37, 39, 39, 39, 39, 42, 42, 45

Offset

1,1

Comments

Facilitates the computing of A126917.

a(n) grows only when n is a prime. A243498 gives the values at those points.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Formula

For all n, a(n) <= A126917(n+1).

For n >= 2, if A126917(n) > a(n-1) [when n is composite], a(n) = a(n-1).

Example

The first eight terms of A126917 are: 1, 2, 3, 5, 4, 8, 6, 11. In range [1,1] the first that has not yet occurred is 2, in range [1,2] it is 3, in range [1,3] it is 4, in range [1,4] it is still 4, in range [1,5] it is 6, in range [1,6] it is still 6, in range [1,7] it is 7, in range [1,8] it is still 7, thus the first eight terms of this sequence are 2, 3, 4, 4, 6, 6, 7, 7.

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(definec (A243069 n) (cond ((<= n 3) (+ 1 n)) ((= (A126917 n) (A243069 (- n 1))) (let loop ((i (A126917 n))) (if (not-lte? (A126918 i) n) i (loop (+ 1 i))))) (else (A243069 (- n 1)))))
;; 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 which can be found from IntSeq-library):
(define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))

Crossrefs

Cf. A126917, A126918, A243488, A243498.

Sequence in context: A145340 A307989 A160680 * A342496 A061984 A337125

Adjacent sequences: A243066 A243067 A243068 * A243070 A243071 A243072

Keyword

nonn

Author

Antti Karttunen, Jun 20 2014

Status

approved