A126604 a(1) = 4; a(2) = 3; for n > 2, a(n) = a(n-1)^2 + a(n-1) - 1.

4, 3, 11, 131, 17291, 298995971, 89398590973228811, 7992108067998667938125889533702531, 63873791370569400659097694858350356285036046451665934814399129508491

Offset: 1

Author

Tomas Xordan, Jan 06 2007

Keywords

• nonn

Comments

a(n) = -1 + Product_{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 formulas 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.

Examples

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

Crossrefs

Cf. A005267.

Programs

Maple

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, Jan 09 2007

Mathematica

Join[{4},NestList[#^2+#-1&,3,10]] (* Harvey P. Dale, Jul 24 2012 *)

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

Extensions

Edited and extended by Klaus Brockhaus and Emeric Deutsch, Jan 09 2007