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

1,2

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

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

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

Cf. A077113, A077121.

Sequence in context: A114090 A351959 A217843 * A046874 A316416 A303262

Adjacent sequences: A139750 A139751 A139752 * A139754 A139755 A139756

Keyword

nonn

Author

Zak Seidov, May 19 2008

Status

approved