A249053 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 greater than a(n-1), unless a(n) is required to be prime by (ii), in which case a(n) is the smallest unused prime greater than a(n-1).

1, 2, 4, 5, 6, 8, 11, 12, 13, 14, 17, 18, 20, 23, 24, 25, 26, 29, 30, 31, 32, 37, 38, 41, 42, 44, 45, 47, 48, 53, 54, 55, 59, 60, 62, 63, 67, 68, 71, 72, 73, 74, 79, 80, 81, 82, 83, 84, 89, 90, 97, 98, 101, 102, 104, 105, 106, 108, 109, 110, 113, 114, 115

Offset: 1

Author

N. J. A. Sloane, Nov 01 2014

Keywords

• nonn

References

• Eric Angelini, Posting to Sequence Fans Mailing List, Mar 17 2008 (the definition was clarified by Gabriel Cunningham).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

See A249054 for another version.

Cf. A002808, A007918.

Programs

Haskell

import Data.Map (singleton, findMin, delete, insert)
a249053 n = a249053_list !! (n-1)
a249053_list = 1 : f 1 1 a002808_list (singleton 1 1) where
   f x z cs m
     | k == x    = p : f (x + 1) p cs (insert (x + p) 0 $ delete x m)
     | otherwise = c : f (x + 1) c cs' (insert (x + c) 0 m)
     where p = a007918 z
           (c:cs') = dropWhile (<= z) cs
           (k,_) = findMin m
-- Reinhard Zumkeller, Nov 01 2014