cp's OEIS Frontend

A139753 a(2n) = next cube after a(2n-1), a(2n+1) = next square after a(2n).

%I A139753 #6 Feb 09 2022 19:19:56
%S A139753 1,8,9,27,36,64,81,125,144,216,225,343,361,512,529,729,784,1000,1024,
%T A139753 1331,1369,1728,1764,2197,2209,2744,2809,3375,3481,4096,4225,4913,
%U A139753 5041,5832,5929,6859,6889,8000,8100,9261,9409,10648,10816,12167,12321,13824
%N A139753 a(2n) = next cube after a(2n-1), a(2n+1) = next square after a(2n).
%C A139753 Terms with even indices are cubes n^3 with n=2,3,... (all integers >1), while terms with odd indices are square m^3 with m=1,3,6,9,12,15,19,23,28,32,37,42,47,53,59,65,71,77,83,90,97,104,111,118,126,133,141,149,157,165,173,182,190,199,208,217,226,235,244,253,263,273,282,292,302,312,323,333,344,354,365,375,386,397,408,420,431,442,454,465,477,489,501,513,525,537,549,561,574,586,599,611,624,637,650,663,676,689,703,716,730,743,757,770,784,798,812,826,840,854,869,883,897,912,926,941,956,971,986,1001; cf. A077121 Number of integer squares <= n^3.
%H A139753 Harvey P. Dale, <a href="/A139753/b139753.txt">Table of n, a(n) for n = 1..1000</a>
%e A139753 a(1)=1 considered as square,
%e A139753 a(2)=8 = least cube >a(1);
%e A139753 a(3)=9 = least square >a(2),
%e A139753 a(4)=27 = least cube >a(3),
%e A139753 a(5)=36 = least square >a(4),
%e A139753 a(6)=64 = least cube >a(5),
%e A139753 a(7)=81 = least square >a(6),
%e A139753 a(8)=125 = least cube >a(7).
%t A139753 nxt[{n_,a_}]:={n+1,If[OddQ[n],(Floor[Surd[a,3]]+1)^3,(Floor[Sqrt[a]]+1)^2]}; NestList[nxt,{1,1},50][[All,2]] (* _Harvey P. Dale_, Feb 09 2022 *)
%Y A139753 Cf. A077113, A077121.
%K A139753 nonn
%O A139753 1,2
%A A139753 _Zak Seidov_, May 19 2008