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 A249054 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. 5
 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, 37, 25, 26, 41, 27, 43, 28, 47, 30, 32, 53, 59, 33, 34, 61, 67, 35, 36, 71, 38, 73, 39, 40, 79, 83, 42, 89, 97, 101, 44, 45, 103, 46, 48, 107, 49, 50, 109, 113, 51 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. A permutation of the positive integers with inverse A249571. REFERENCES Gabriel Cunningham, Posting to Sequence Fans Mailing List, Mar 17 2008. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 EXAMPLE a(7) = 5, so a(7+a(7)) = a(7+5) = a(12) = 11 must be prime, which it is. PROG (Haskell) import Data.Map (singleton, findMin, delete, insert) a249054 n = a249054_list !! (n-1) a249054_list = 1 : f 1 a000040_list a002808_list (singleton 1 1) where    f x ps'@(p:ps) cs'@(c:cs) m      | k == x    = p : f (x + 1) ps cs' (insert (x + p) 0 \$ delete x m)      | otherwise = c : f (x + 1) ps' cs (insert (x + c) 0 m)      where (k, _) = findMin m -- Reinhard Zumkeller, Nov 01 2014 CROSSREFS See A249053 for another version. Cf. A000040, A002808, A249571 (inverse). Positions of primes and nonprimes: A249594 and A249595. Sequence in context: A296616 A143529 A261351 * A103867 A075375 A191670 Adjacent sequences:  A249051 A249052 A249053 * A249055 A249056 A249057 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 01 2014 EXTENSIONS Data corrected by Reinhard Zumkeller, Nov 01 2014 STATUS approved

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Last modified March 26 23:02 EDT 2019. Contains 321565 sequences. (Running on oeis4.)