A249595 -id:A249595 - cp's OEIS frontend

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

N. J. A. Sloane, Nov 01 2014

nonn

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.

			a(7) = 5, so a(7+a(7)) = a(7+5) = a(12) = 11 must be prime, which it is.

Gabriel Cunningham, Posting to Sequence Fans Mailing List, Mar 17 2008.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

See A249053 for another version.
Cf. A000040, A002808, A249571 (inverse).
Positions of primes and nonprimes: A249594 and A249595.

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

Data corrected by Reinhard Zumkeller, Nov 01 2014

A249594 Positions of primes in A249054.

Original entry on oeis.org

2, 4, 7, 11, 12, 14, 17, 18, 19, 22, 23, 27, 30, 32, 34, 37, 38, 41, 42, 45, 47, 50, 51, 53, 54, 55, 58, 61, 64, 65, 68, 71, 72, 74, 75, 78, 80, 81, 84, 87, 89, 90, 94, 97, 100, 102, 105, 108, 109, 111, 113, 116, 117, 119, 120, 123, 125, 129, 133, 134, 135

Offset: 1

Reinhard Zumkeller, Nov 03 2014

nonn

A249054(a(n)) = A000040(n); sequence is strictly increasing, i.e. all primes occur in A249054 in natural order, see also A249595.

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

Cf. A000040, A026233, A049084, A239968, A249054, A249595 (complement).

import Data.List (elemIndex); import Data.Maybe (fromJust)
a249594 = (+ 1) . fromJust . (`elemIndex` a249054_list) . a000040

cp's OEIS Frontend

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.

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