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

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

Offset

0,1

Comments

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

Links

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 + ...

Formula

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A003096, A007814, A153893, A260315.

Sequence in context: A195569 A118908 A153060 * A369727 A090115 A051999

Adjacent sequences: A139241 A139242 A139243 * A139245 A139246 A139247

Keyword

easy,nonn,changed

Author

Jonathan Vos Post, Jun 06 2008

Status

approved