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A260933
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Lexicographically smallest permutation of the natural numbers, such that a(n)+n and a(n)+n+1 are both composite numbers.
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3
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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
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listen;
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OFFSET
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1,1
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COMMENTS
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The permutation is self-inverse: a(a(n)) = n.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers
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MATHEMATICA
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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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PROG
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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
(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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CROSSREFS
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Cf. A010051, A002808, A136798, A260936 (fixed points), A260822.
Sequence in context: A284807 A309909 A031099 * A194755 A333884 A055118
Adjacent sequences: A260930 A260931 A260932 * A260934 A260935 A260936
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Aug 04 2015
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STATUS
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approved
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