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
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
Programs
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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
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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