%I #14 Dec 13 2014 00:40:23

%S 1,1,2,1,3,2,5,1,4,3,7,2,11,5,6,1,13,4,17,3,8,7,19,2,9,11,10,5,23,6,

%T 29,1,12,13,15,4,31,17,14,3,37,10,41,7,16,19,43,2,25,9,18,11,47,8,21,

%U 5,20,23,53,6,59,29,22,1,27,14,61,13,24,15,67,4,71,31,26,17,35,22,73,3,28,37,79,10,33,41,30,7,83,12,55,19,32,43,39,2,89,25,34,9,97,26,101

%N a(n) = A249817(A064989(A249818(n))).

%C Odd bisection, A250472, is a permutation of natural numbers. A250479 gives the even bisection.

%C For odd numbers n >= 3, a(n) = A078898(n)-th number k for which A055396(k) = A055396(n)-1. In other words, a(n) tells which number is located immediately above n in the sieve of Eratosthenes (see A083140, A083221) in the same column of the sieve that contains n.

%H Antti Karttunen, <a href="/A250470/b250470.txt">Table of n, a(n) for n = 1..9048</a>

%F a(n) = A249817(A064989(A249818(n))).

%F Other identities. For all n >= 1:

%F a(A250469(n)) = n. [This is an inverse function for injection A250469.]

%F For all odd numbers n >= 3: A055396(a(n)) = A055396(n)-1.

%o (Scheme) (define (A250470 n) (A249817 (A064989 (A249818 n))))

%Y Cf. A055396, A064989, A078898, A083140, A083221, A249744, A249810, A249820, A249817, A249818, A250469.

%Y Odd bisection: A250472.

%Y Even bisection: A250479.

%Y Differs from A064989 for the first time at n=21, where a(21) = 8, while

%Y A064989(21) = 10.

%K nonn

%O 1,3

%A _Antti Karttunen_, Dec 06 2014