1,1

a(n) = -1 + Prod_{k=1..n-1}a(k) for n>1.

Sequence is a variant of A005267 (start values 3 and 2, offset 0). Both sequences have the same recursion formulae and both are infinite coprime sequences; a(n) has digital root 2 for odd n and 5 for even n, n > 2.

a(2) to a(6) are prime, a(1) and a(7) to a(10) are composite, a(2) to a(10) are squarefree.

a(3) = 3^2+3-1 = 11, a(4) = 11^2+11-1 = 131.

a[1]:=1: a[2]:=3: for n from 3 to 10 do a[n]:=a[n-1]^2+a[n-1]-1 od: seq(a[n], n=1..10); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 09 2007

(PARI) 1. {print1(4, ", ", a=3, ", "); for(n=1, 8, print1(a=a^2+a-1, ", "))}

2. {m=10; v=vector(m); print1(v[1]=4, ", "); for(n=2, m, print1(v[n]=-1+prod(k=1, n-1, v[k]), ", "))} - Klaus Brockhaus, Jan 09 2007

Cf. A005267.

Adjacent sequences: A126601 A126602 A126603 this_sequence A126605 A126606 A126607

Sequence in context: A065337 A072802 A093726 this_sequence A099377 A121844 A091512

nonn

Tomas Xordan (xordan.tom(AT)gmail.com), Jan 06 2007

Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 09 2007