A128827 Perfect powers beginning and ending with the same digit.

1, 4, 8, 9, 121, 343, 484, 676, 1331, 1521, 1681, 4624, 5625, 9409, 10201, 11881, 12321, 14161, 14641, 16641, 17161, 19321, 19881, 21952, 40804, 43264, 44944, 47524, 49284, 50625, 55225, 60516, 64516, 65536, 69696, 79507, 91809, 94249

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

97^2 = 9409 is a term; 43^3 = 79507 is a term.

Mathematica

Join[{1}, Select[Range[2, 10^5], First[IntegerDigits[#]]==Last[IntegerDigits[#]]&&ResourceFunction["PerfectPowerQ"][#]&]] (* James C. McMahon, Jan 11 2025 *)

Prog

(Magma) PP:=[1] cat [ n: n in [2..100000] | IsPower(n) ]; [ n: n in PP | k[1] eq k[ #k] where k is Intseq(n, 10) ]; // Klaus Brockhaus, Apr 16 2007

Crossrefs

Cf. A001597 (perfect powers), A075786 (palindromic perfect powers), A129450.

Sequence in context: A327654 A110811 A226035 * A075786 A348429 A046450

Adjacent sequences: A128824 A128825 A128826 * A128828 A128829 A128830

Keyword

nonn,base

Author

J. M. Bergot, Apr 12 2007

Extensions

Edited, corrected and extended by Klaus Brockhaus, Apr 16 2007

Status

approved