A102846 a(0)=1, a(1)=1, a(n) = a(n-1)*a(n-2) + 2.

1, 1, 3, 5, 17, 87, 1481, 128849, 190825371, 24587658227981, 4691949003375676905953, 115364038518117215020660724770070895, 541282185550473269502054702460138578085934426170057537937

Offset

0,3

Comments

Prime for n=2,3,4 (a Fermat prime each time); prime for n=6. When is the next prime in the sequence? Semiprime for a(5) = 87 = 3 * 29, a(10) = 127 * 36944480341540763039. a(11) has 36 digits and is the product of 6 primes. a(12) has 57 digits and is the product of 4 primes. a(13) has 92 digits and is the product of at least 4 primes: 123419 * 35173043 * 80-digit-composite, with the second-smallest prime divisor starting with the concatenation of a(2),a(3),a(4). - Jonathan Vos Post, Feb 28 2005

Links

Table of n, a(n) for n=0..12.

Example

a(4)=17, a(5)=87, a(6) = 17*87 + 2 = 1481.

Maple

a[0]:=1: a[1]:=1: for n from 2 to 13 do a[n]:=a[n-1]*a[n-2]+2 od: seq(a[n], n=0..13); # Emeric Deutsch, Mar 08 2005

Crossrefs

Sequence in context: A227335 A351718 A281627 * A100003 A283331 A114161

Adjacent sequences: A102843 A102844 A102845 * A102847 A102848 A102849

Keyword

easy,nonn

Author

Miklos Kristof, Feb 28 2005

Extensions

More terms from Emeric Deutsch, Mar 08 2005

Status

approved