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A113769 a(1) = 1, a(n+1) = a(n) + round(a(n)^(1/3)).

%I A113769 #15 Dec 29 2023 13:15:12
%S A113769 1,2,3,4,6,8,10,12,14,16,19,22,25,28,31,34,37,40,43,47,51,55,59,63,67,
%T A113769 71,75,79,83,87,91,95,100,105,110,115,120,125,130,135,140,145,150,155,
%U A113769 160,165,170,176,182,188,194,200,206,212,218,224,230,236,242,248,254
%N A113769 a(1) = 1, a(n+1) = a(n) + round(a(n)^(1/3)).
%C A113769 A033638 a(0) = 1; a(1) = 1; for n > 1 a(n) = a(n-1) + round(sqrt(a(n-1))). Hence the current sequence is analogous to A033638, but with cube root instead of square root.
%H A113769 Harvey P. Dale, <a href="/A113769/b113769.txt">Table of n, a(n) for n = 1..1000</a>
%F A113769 a(1) = 1, a(n+1) = a(n) + round(a(n)^(1/3)).
%e A113769 a(19) = 43, so a(20) = a(19) + round(a(19)^(1/3)) = 43 + round(43^(1/3)) = 43 + round(3.50339806) = 43 + 4 = 47.
%e A113769 a(31) = 91, so a(32) = a(31) + round(a(31)^(1/3)) = 91 + round(4.49794145) = 91 + 4 = 95.
%e A113769 a(32) = 95, so a(33) = a(32) + round(a(32)^(1/3)) = 95 + round(4.56290264) = 95 + 5 = 100.
%e A113769 a(47) = 170, so a(48) = 170 + round(170^(1/3)) = 170 + round(5.53965826) = 176.
%t A113769 NestList[#+Round[Surd[#,3]]&,1,60] (* _Harvey P. Dale_, Jan 12 2019 *)
%Y A113769 Cf. A033638, A113768 (flooring instead rounding).
%K A113769 easy,nonn
%O A113769 1,2
%A A113769 _Jonathan Vos Post_, Jan 19 2006