A121217 a(1)=1, a(2)=2, a(3)=3; for n > 3, a(n) is the smallest positive integer which does not occur earlier in the sequence and which is not coprime to a(n-2).

1, 2, 3, 4, 6, 8, 9, 10, 12, 5, 14, 15, 7, 18, 21, 16, 24, 20, 22, 25, 11, 30, 33, 26, 27, 13, 36, 39, 28, 42, 32, 34, 38, 17, 19, 51, 57, 45, 48, 35, 40, 49, 44, 56, 46, 50, 23, 52, 69, 54, 60, 58, 55, 29, 65, 87, 70, 63, 62, 66, 31, 64, 93, 68, 72, 74, 75, 37, 78, 111, 76, 81

Offset: 1

Author

Leroy Quet, Aug 20 2006

Keywords

• nonn

Comments

Conjecture: this is a permutation of the positive integers, cf. A256618. - Reinhard Zumkeller, Apr 05 2015

The B-sequence mentioned in the Maple program is not in the OEIS. It is 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, ... - Alois P. Heinz, Feb 02 2019

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..20632

Crossrefs

Cf. A064413, A121216, A251622, A256414 (indices of primes), A256419 (smoothed version).

Cf. A256618 (conjectured inverse).

Programs

Haskell

a121217 n = a121217_list !! (n-1)
a121217_list = 1 : 2 : 3 : f 2 3 [4..] where
   f u v xs = g xs where
     g (w:ws) = if gcd w u > 1 then w : f v w (delete w xs) else g ws
-- Reinhard Zumkeller, Apr 05 2015

Maple

# From N. J. A. Sloane, Apr 04 2015: A121217 gcd(A[n],A[n-2])>1 A=seq, for B see the COMMENTS
N:= 60: # to get a(1) to a(n) where a(n+1) is the first term > N
B:= Vector(N, datatype=integer[4]):
for n from 1 to 3 do A[n]:= n: od:
for n from 4 do
  for k from 4 to N do
    if B[k] = 0 and igcd(k, A[n-2]) > 1 then
       A[n]:= k;
       B[k]:= 1;
       break
    fi
  od:
  if k > N then break fi
od:
[seq(A[i], i=1..n-1)];

Mathematica

a = Range@ 3; Do[k = 4; While[Or[MemberQ[a, k], CoprimeQ[a[[i - 2]], k]], k++]; AppendTo[a, k], {i, 4, 72}]; a (* Michael De Vlieger, Aug 19 2017 *)

Extensions

Extended by Ray Chandler, Aug 22 2006