|
%I #13 Jun 21 2014 14:18:50
%S 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,
%T 16,19,19,21,21,21,21,21,21,22,22,22,22,27,27,28,28,28,28,30,30,30,30,
%U 30,30,31,31,31,31,31,31,36,36,37,37,37,37,37,37,39,39,39,39,42,42,45
%N a(n) = smallest natural number that has not yet occurred among the first n terms of A126917.
%C Facilitates the computing of A126917.
%C a(n) grows only when n is a prime. A243498 gives the values at those points.
%H Antti Karttunen, <a href="/A243069/b243069.txt">Table of n, a(n) for n = 1..10000</a>
%F For all n, a(n) <= A126917(n+1).
%F For n >= 2, if A126917(n) > a(n-1) [when n is composite], a(n) = a(n-1).
%e 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.
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (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)))))
%o ;; We consider a > b (i.e. not less than b) also in case a is nil.
%o ;; (Because of the stateful caching system used by defineperm1-macro which can be found from IntSeq-library):
%o (define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))
%Y Cf. A126917, A126918, A243488, A243498.
%K nonn
%O 1,1
%A _Antti Karttunen_, Jun 20 2014
|
