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Perfect powers beginning and ending with the same digit.
2

%I #12 Jan 11 2025 20:56:53

%S 1,4,8,9,121,343,484,676,1331,1521,1681,4624,5625,9409,10201,11881,

%T 12321,14161,14641,16641,17161,19321,19881,21952,40804,43264,44944,

%U 47524,49284,50625,55225,60516,64516,65536,69696,79507,91809,94249

%N Perfect powers beginning and ending with the same digit.

%H Michael De Vlieger, <a href="/A128827/b128827.txt">Table of n, a(n) for n = 1..10000</a>

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

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

%o (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

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

%K nonn,base

%O 1,2

%A _J. M. Bergot_, Apr 12 2007

%E Edited, corrected and extended by _Klaus Brockhaus_, Apr 16 2007