A139244 -id:A139244 - cp's OEIS frontend

A260315 Decimal expansion of the generating constant c of A139244.

1, 9, 6, 6, 8, 9, 1, 7, 6, 1, 7, 9, 0, 1, 7, 6, 3, 6, 5, 3, 3, 3, 5, 0, 5, 7, 2, 0, 2, 2, 6, 6, 9, 8, 2, 7, 6, 1, 3, 2, 2, 1, 2, 1, 1, 8, 6, 8, 6, 3, 3, 5, 3, 4, 2, 2, 0, 1, 8, 5, 8, 2, 8, 8, 3, 1, 2, 6, 2, 5, 6, 4, 4, 2

Offset: 1

Chayim Lowen, Jul 22 2015

A139244(n-1) = ceiling(c^(2^n)).

The digit 4 appears for the first time only at position n=53, making it the last one to appear in the sequence.

			1.96689176179017636533350572... .

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!)

Cf. A139244.

A003096 a(n) = a(n-1)^2 - 1, a(0) = 2.

Original entry on oeis.org

2, 3, 8, 63, 3968, 15745023, 247905749270528, 61457260521381894004129398783, 3776994870793005510047522464634252677140721938309041881088

Offset: 0

N. J. A. Sloane

After a(0) = 2 and a(1) = 3, this can never be prime, since a(n) = (a(n-1) + 1) * (a(n-1) - 1). Each term is relatively prime to its successor. - Jonathan Vos Post, Jun 06 2008

Mensa (see Dutch link below) indicates high intelligence by offering a self test containing a number of problems, one of which is "Complete each series with the element that logically continues the series: 3968, 63, 8, 3". - David A. Corneth, May 19 2024

R. K. Guy, How to factor a number, Proc. 5th Manitoba Conf. Numerical Math., Congress. Num. 16 (1975), 49-89.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G. C. Greubel, Table of n, a(n) for n = 0..12
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!)
Mensa, self-test indicative for high IQ
Index entries for sequences of form a(n+1)=a(n)^2 + ...

Cf. A003095, A077124, A139244.

[n le 1 select 2 else Self(n-1)^2 -1: n in [1..12]]; // G. C. Greubel, Oct 27 2022

a := proc(n) local k, v: v := 2: for k from 1 to n do v := v^2-1: od: v: end:
seq(a(n), n = 0 .. 8); # Lorenzo Sauras Altuzarra, Feb 01 2023

NestList[#^2-1&,2,10] (* Harvey P. Dale, Nov 06 2011 *)

PARI
```
a(n)=if(n<1,2*(n==0),a(n-1)^2-1)
```

def A003096(n): return 2 if (n==0) else A003096(n-1)^2 -1
[A003096(n) for n in range(12)] # G. C. Greubel, Oct 27 2022

a(n-1) = ceiling(c^(2^n)) where c = 1.295553... = A077124. - Benoit Cloitre, Nov 29 2002

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A260315 Decimal expansion of the generating constant c of A139244.

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A003096 a(n) = a(n-1)^2 - 1, a(0) = 2.

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