A361086 a(n) = a(n-1)*(a(n-1)^2 - 1) with a(0) = 2.
2, 6, 210, 9260790, 794226015149981778210, 500993769952171221242360491304282624082148055373236400176882790
Offset: 0
Examples
After a(0) = 2, we have: a(1) = a(0) * 3 = 6 = A002110(2), a(2) = a(1) * 5 * 7 = 210 = A002110(4), a(3) = a(2) * 11 * 19 * 211 = A002110(5) * 19 * 211, a(4) = a(3) * 23 * 137 * 2939 * 101 * 91691, (*) a(5) = a(4) * 2381 * 4547 * 73360073674487 * 4111 * 9463 * 20415865295227, (*) a(6) = a(5) * (a(5)-1) * (a(5)+1) where a(5)-1 = 8297 * 2809343 * 1697219017859557 * 12663932268383565339458540396093810087 and a(5)+1 = 6529 * 11220511276757421196620288973 * 6838691459094922770231096737923, etc. (*) We list first the prime factors of a(n-1)-1, then those of a(n-1)+1.
Links
- Winston de Greef, Table of n, a(n) for n = 0..7
- Dan Asimov, Interesting sequence on MathOverflow, math-fun mailing list (access restricted to subscribers), Mar 28 2023.
- Fredrick M. Nelson, Does a(0)=6, a(n+1)=a(n)^3-a(n), define a square-free sequence?, MathOverflow, Mar 24 2023.
Programs
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Maple
a:= proc(n) option remember; procname(n-1)*(procname(n-1)-1)*(procname(n-1)+1) end proc: a(0):= 2: seq(a(i),i=0..7); # Robert Israel, Apr 16 2023
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Mathematica
RecurrenceTable[{a[n] == a[n-1]*(a[n-1]^2 - 1), a[0] == 2}, a, {n, 0, 6}] (* Vaclav Kotesovec, Apr 13 2023 *) -
PARI
A361086_first(N)=vector(N,i,N=if(i>1,N*(N^2-1),2))
Formula
a(n) ~ c^(3^n), where c = 1.8114401993215336517307679103877676944735007990106818615618948774060863424... - Vaclav Kotesovec, Apr 13 2023
Comments