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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

a(n+1) = a(n)^2 -a(n) + 1 for n >2.

1/3=1/4+1/13+1/157+1/24493+...1/a(n) n->Infinity or 1=3/4+3/13+3/157+3/24493+...3/a(n) n->Infinity [From Artur Jasinski, Sep 21 2008]

1/3=Sum[1/a[n+2],{n,1,Infinity}]=1/4+1/13+1/157+1/24493+...1/a(n) n->Infinity or 1=Sum[3/a[n+2],{n,1,Infinity}]=3/4+3/13+3/157+3/24493+...3/a(n) n->Infinity. If we take segment of length 1 and we will be cut off in each step fragment maximal length such that numerator of fraction is 3, denominators of such fractions will be successive numbers of this sequence. [From Artur Jasinski, Sep 22 2008]

a(n+2)=1.8806785436830780944921917650127503562630617563236301969047995953391\

4798717695395204087358090874194124503892563356447954254847544689332763...^(2^n) [From 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 [From Artur Jasinski, Sep 22 2008]

CROSSREFS

Cf. A000058.

A000058, A082732, A144743, A144779, A144780, A144781, A144782, A144783, A144784, A144785, A144786, A144787, A144788 [From Artur Jasinski, Sep 22 2008]

Sequence in context: A122151 A294384 A216868 * A220846 A009286 A076663

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 January 19 16:32 EST 2019. Contains 319309 sequences. (Running on oeis4.)