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

1,2

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

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 *)

Prog

(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

Crossrefs

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

Cf. A256618 (conjectured inverse).

Sequence in context: A184899 A039034 A047302 * A357992 A255582 A254077

Adjacent sequences: A121214 A121215 A121216 * A121218 A121219 A121220

Keyword

nonn

Author

Leroy Quet, Aug 20 2006

Extensions

Extended by Ray Chandler, Aug 22 2006

Status

approved