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

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

Offset: 1

Author

Zak Seidov, May 19 2008

Keywords

• nonn

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.

Examples

			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).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A077113, A077121.

Programs

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 *)