

A139753


a(2n) = next cube after a(2n1), a(2n+1) = next square after a(2n).


1



1, 8, 9, 27, 36, 64, 81, 125, 144, 216, 225, 343, 361, 512, 529, 729, 784, 1000, 1024, 1331, 1369, 1728, 1764, 2197, 2209, 2744, 2809, 3375, 3481, 4096, 4225, 4913, 5041, 5832, 5929, 6859, 6889, 8000, 8100, 9261, 9409, 10648, 10816, 12167, 12321, 13824
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OFFSET

1,2


COMMENTS

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.


LINKS



EXAMPLE

a(1)=1 considered as square,
a(2)=8 = least cube >a(1);
a(3)=9 = least square >a(2),
a(4)=27 = least cube >a(3),
a(5)=36 = least square >a(4),
a(6)=64 = least cube >a(5),
a(7)=81 = least square >a(6),
a(8)=125 = least cube >a(7).


MATHEMATICA

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 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



