A186750 a(0) = 3; thereafter, a(n) = a(n-1)^2 - 3.

3, 6, 33, 1086, 1179393, 1390967848446, 1934791555410494424614913, 3743418362887760317407541271559358491868341997566

Offset: 0

Author

Jonathan Vos Post, Feb 26 2011

Keywords

• nonn
• easy

Comments

This is to A001566 as 3 is to 2 (subtrahend). Unlike A001566, which begins with 4 consecutive primes, this sequence can never be prime after a(0) = 3, because the first two terms are both multiples of 3, hence all later terms are. This is the k = 3 row of the array A(k, 0) = 3, A(k, n) = A(k, n-1)^2 - k; and A001566 is the k = 2 row. A003096(n+1) is the k = 1 row.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..11
• Index entries for sequences of form a(n+1)=a(n)^2 + ...

Crossrefs

Cf. A001566, A003096.

Programs

Mathematica

RecurrenceTable[{a[0] == 3, a[n] == a[n-1]^2 - 3}, a, {n, 0, 10}] (* Vaclav Kotesovec, Dec 18 2014 *)
Drop[Abs[NestList[#^2 - 3 &, 0, 9]], 1] (* Alonso del Arte, Apr 08 2016 *)

Formula

a(n) ~ c^(2^n), where c = 2.3959550115176494685408322564302422183669584045032057908382914927198090627... - Vaclav Kotesovec, Dec 18 2014