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A139244 a(0) = 4; a(n) = a(n-1)^2 - 1. 3
4, 15, 224, 50175, 2517530624, 6337960442777829375, 40169742574216538983356186036612890624, 1613608218478824775913354216413699241125577233045500390244103887844987109375 (list; graph; refs; listen; history; text; internal format)
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, The Fibonacci Quarterly, 11 (1973), 429-437.

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 * A090115 A051999 A048731

Adjacent sequences:  A139241 A139242 A139243 * A139245 A139246 A139247

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jun 06 2008

STATUS

approved

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Last modified April 25 23:48 EDT 2019. Contains 322465 sequences. (Running on oeis4.)