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A082732 a(1) = 1, a(2) = 3, a(n) = LCM of all the previous terms + 1. 21
1, 3, 4, 13, 157, 24493, 599882557, 359859081592975693, 129498558604939936868397356895854557, 16769876680757063368089314196389622249367851612542961252860614401811693 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The LCM is in fact the product of all previous terms. From a(5) onwards the terms alternately end in 57 and 93.

LINKS

Table of n, a(n) for n=1..10.

FORMULA

For n>=3, a(n+1) = a(n)^2 - a(n) + 1.

For n>=3, a(n) = A004168(n-3) + 1. - Max Alekseyev, Aug 09 2019

1/3 = Sum_{n=3..oo} 1/a(n) = 1/4 + 1/13 + 1/157 + 1/24493 + ... or 1 = Sum_{n=3..oo} 3/a(n) = 3/4 + 3/13 + 3/157 + 3/24493 + .... If we take segment of length 1 and cut off in each step fragment of maximal length such that numerator of fraction is 3, denominators of such fractions will be successive numbers of this sequence. - Artur Jasinski, Sep 22 2008

a(n+2)=1.8806785436830780944921917650127503562630617563236301969047995953391\

4798717695395204087358090874194124503892563356447954254847544689332763...^(2^n). -  Artur Jasinski, Sep 22 2008

MATHEMATICA

a[1] = 1; a[2] = 3; a[n_] := Apply[LCM, Table[a[i], {i, 1, n - 1}]] + 1; Table[ a[n], {n, 1, 10}]

c=1.8806785436830780944921917650127503562630617563236301969047995953391479871\

7695395204087358090874194124503892563356447954254847544689332763; Table[c^(2^n), {n, 1, 6}] or a = {}; k = 4; Do[AppendTo[a, k]; k = k^2 - k + 1, {n, 1, 10}]; a (* Artur Jasinski, Sep 22 2008 *)

CROSSREFS

Cf. A000058, A004168, A144743, A144779, A144780, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788.

Sequence in context: A122151 A294384 A216868 * A307893 A220846 A009286

Adjacent sequences:  A082729 A082730 A082731 * A082733 A082734 A082735

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Apr 14 2003

EXTENSIONS

More terms from Robert G. Wilson v, Apr 15 2003

STATUS

approved

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)