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%I #29 Nov 04 2014 05:58:12
%S 1,2,4,3,6,8,5,9,10,12,7,11,14,13,15,16,17,19,23,18,20,29,31,21,22,24,
%T 37,25,26,41,27,43,28,47,30,32,53,59,33,34,61,67,35,36,71,38,73,39,40,
%U 79,83,42,89,97,101,44,45,103,46,48,107,49,50,109,113,51
%N Defined by (i) a(1)=1; (ii) if you move a(n) steps to the right you must reach a prime; (iii) a(n) = smallest unused composite number, unless a(n) is required to be prime by (ii), in which case a(n) is the smallest unused prime.
%C In contrast to A249053, here all the primes appear and in the correct order, and all the composites appear, also in increasing order. The graph shows two distinct curves. In A249053 many terms are missing, and the points lie on a single curve.
%C A permutation of the positive integers with inverse A249571.
%D Gabriel Cunningham, Posting to Sequence Fans Mailing List, Mar 17 2008.
%H Reinhard Zumkeller, <a href="/A249054/b249054.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e a(7) = 5, so a(7+a(7)) = a(7+5) = a(12) = 11 must be prime, which it is.
%o (Haskell)
%o import Data.Map (singleton, findMin, delete, insert)
%o a249054 n = a249054_list !! (n-1)
%o a249054_list = 1 : f 1 a000040_list a002808_list (singleton 1 1) where
%o f x ps'@(p:ps) cs'@(c:cs) m
%o | k == x = p : f (x + 1) ps cs' (insert (x + p) 0 $ delete x m)
%o | otherwise = c : f (x + 1) ps' cs (insert (x + c) 0 m)
%o where (k,_) = findMin m
%o -- _Reinhard Zumkeller_, Nov 01 2014
%Y See A249053 for another version.
%Y Cf. A000040, A002808, A249571 (inverse).
%Y Positions of primes and nonprimes: A249594 and A249595.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Nov 01 2014
%E Data corrected by _Reinhard Zumkeller_, Nov 01 2014
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