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.

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

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

Index entries for sequences that are permutations of the natural numbers

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: A143529 A331010 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