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
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Programs
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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 *)
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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
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