A260933 Lexicographically smallest permutation of the natural numbers, such that a(n)+n and a(n)+n+1 are both composite numbers.

7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 13, 18, 17, 16, 15, 14, 19, 24, 23, 22, 21, 20, 25, 28, 27, 26, 33, 32, 31, 30, 29, 34, 39, 38, 37, 36, 35, 40, 43, 42, 41, 46, 45, 44, 47, 50, 49, 48, 53, 52, 51, 56, 55, 54, 57, 58, 59, 60, 61, 62, 65, 64, 63, 66, 67

Offset: 1

Author

Reinhard Zumkeller, Aug 04 2015

Keywords

• nonn

Comments

The permutation is self-inverse: a(a(n)) = n.

Links

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

Crossrefs

Cf. A010051, A002808, A136798, A260936 (fixed points), A260822.

Programs

Haskell

import Data.List (delete)
a260933 n = a260933_list !! (n-1)
a260933_list = f 1 [1..] where
   f x zs = g zs where
     g (y:ys) = if a010051' (x + y) == 0 && a010051' (x + y + 1) == 0
                   then y : f (x + 1) (delete y zs) else g ys

Mathematica

a[n_]:=a[n]=(k=1;While[PrimeQ[k+n]||PrimeQ[k+n+1]||MemberQ[Array[a,n-1],k],k++];k);Array[a,100] (* Giorgos Kalogeropoulos, Jul 06 2021 *)

Python

from sympy import isprime
def composite(n): return n > 1 and not isprime(n)
def aupton(terms):
    alst, aset = [], set()
    for n in range(1, terms+1):
        an = 1
        while True:
            while an in aset: an += 1
            if composite(an+n) and composite(an+n+1): break
            an += 1
        alst, aset = alst + [an], aset | {an}
    return alst
print(aupton(67)) # Michael S. Branicky, Jul 06 2021