A260315 -id:A260315 - cp's OEIS frontend

4, 15, 224, 50175, 2517530624, 6337960442777829375, 40169742574216538983356186036612890624, 1613608218478824775913354216413699241125577233045500390244103887844987109375

Offset: 0

Jonathan Vos Post, Jun 06 2008

This is the next analog of A003096 with different initial value a(0), as starting with a(0) = 2 is A003096 and a(0) = 3 is A003096 with first term omitted. It alternates between even and odd values, specifically between 4 mod 10 and 5 mod 10 and is always composite (by difference of squares factorization).

a(n+2) is divisible by a(n)^2. A007814(a(2 n)) = A153893(n). - Robert Israel, Jul 20 2015

Robert Israel, Table of n, a(n) for n = 0..10
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
Index entries for sequences of form a(n+1)=a(n)^2 + ...

Cf. A003096, A007814, A153893, A260315.

A[0]:= 4:
for n from 1 to 10 do A[n]:= A[n-1]^2-1 od:
seq(A[i],i=0..10); # Robert Israel, Jul 20 2015

a=4; lst={a}; Do[b=a^2-1; AppendTo[lst,b]; a=b, {n,10}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 28 2010 *)

a(n)=if(n,a(n-1)^2-1,4) \\ Charles R Greathouse IV, Jul 23 2015

a(n-1) = ceiling(c^(2^n)) where c is a constant between 1 and 2.

More specifically, c=1.9668917617901763653335057202... (sequence A260315). - Chayim Lowen, Jul 17 2015

cp's OEIS Frontend

A139244 a(0) = 4; a(n) = a(n-1)^2 - 1.

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