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

Author

J. M. Bergot, Apr 12 2007

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

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

Programs

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

Mathematica

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

Extensions

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