A109845 a(1) = 2; a(2n) = least common multiple of all previous terms + 1. a(2n+1) = least common multiple of all previous terms - 1.

2, 3, 5, 31, 929, 863971, 746445024869, 557180175152428473492031, 310449747582890872093779269721785644810947012929, 96379045774280656880008037888192772255684941220159788508646084243678677683026025975278640171971

Offset

1,1

Comments

For n > 2 a(2n) == 1 mod 10 and a(2n+1) == 9 mod 10. Conjecture : There are infinitely many primes in this sequence.

Number of decimal digits of a(n): 1, 1, 1, 2, 3, 6, 12, 24, 48, 95, 190, 380, 760, 1520, 3040, 6079, 12158, 24316, 48632, 97264, …, . - Robert G. Wilson v, Jun 19 2016

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..13

Formula

a(2n) = 1+ Product_{n=1..2n-1} a(k). a(2n+1) = -1 + Product_{n=1..2n} a(k).

a(1)=2, a(2)=3 and a(n)=a(n-1)^2+(-1)^n*a(n-1)+(-1)^n for n>=3. - Walter Kehowski, Aug 15 2005

Maple

a[1]:=2: for n from 1 to 5 do a[2*n]:=1+lcm(seq(a[i], i=1..2*n-1)); a[2*n+1]:=-1+lcm(seq(a[j], j=1..2*n)): od: seq(a[n], n=1..10); # Emeric Deutsch, Aug 06 2005
a := proc(n) option remember; if n=1 then 2 elif n=2 then 3 else a(n-1)^2 + (-1)^n*a(n-1) + (-1)^n fi end: # Walter Kehowski, Aug 15 2005

Mathematica

f[n_] := If[OddQ@ n, Fold[LCM, 1, Array[f, n - 1]] - 1, Fold[LCM, 1, Array[f, n - 1]] + 1]; f[1] = 2; Array[f, 10] (* Robert G. Wilson v, Jun 19 2016 *)

Crossrefs

Sequence in context: A106308 A036797 A163079 * A241722 A276043 A041019

Adjacent sequences: A109842 A109843 A109844 * A109846 A109847 A109848

Keyword

easy,nonn

Author

Amarnath Murthy, Jul 06 2005

Extensions

More terms from Emeric Deutsch, Aug 06 2005

Status

approved