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The next square after a(n)^3 is a(n+1)^2.
3

%I #19 Jan 13 2022 18:35:37

%S 1,2,3,6,15,59,454,9674,951501,928140821,28276184777782,

%T 150359618976700758746,1843727887745124274995859697327,

%U 2503486403859294888221025578988349446337176495,125261571430858575370252424686453280425035047529321451018103304969551

%N The next square after a(n)^3 is a(n+1)^2.

%H Harry J. Smith, <a href="/A059842/b059842.txt">Table of n, a(n) for n = 1..21</a>

%F a(n+1) = min { i | i^2 > a(n)^3 }.

%F a(n+1) = floor(sqrt(a(n)^3)) + 1. - _Robert G. Wilson v_, Mar 22 2001

%e a(4) = 6 has cube 216. The next square is 225 = 15^2. So a(5) = 15.

%p a := proc(n) option remember: if n=1 then RETURN(1) fi: if n=2 then RETURN(2) fi: ceil(a(n-1)^((3.)/(3-1))): end: Digits := 200: for n from 1 to 20 do printf(`%a,`,a(n)) od:

%t f[n_Integer] := Floor[ N[ Sqrt[n^3] ] ] + 1; NestList[f, 1, 15]

%o (PARI) { a=0; for (n=1, 21, write("b059842.txt", n, " ", a=floor(sqrt(a^3)) + 1); ) } \\ _Harry J. Smith_, Jun 29 2009

%K nonn

%O 1,2

%A _Rainer Rosenthal_, Feb 26 2001

%E More terms from _James A. Sellers_, Mar 15 2001