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a(n) = least perfect power m that is the sum of n consecutive perfect powers, or -1 if m does not exist.
1

%I #31 Feb 25 2024 22:49:48

%S 1,25,441,100,169,289,121,2395417249

%N a(n) = least perfect power m that is the sum of n consecutive perfect powers, or -1 if m does not exist.

%C It is conjectured that m always exists.

%C The present state of knowledge (with ? for unknown entries) is:

%C 1, 25, 441, 100, 169, 289, 121, 2395417249, ?, 15386237159377984, 676, 232324, ?, ?, ?, 64866916, 3721, 3622354596, 279936, ?, ?, 41152225, 29929, 2137444, ?, 11526025, 97969, 9922500, ?, 978626089, ?, 347151424, ?

%C Known solutions < 10^12 from _J. Stauduhar_. All others from _Tim Peters_.

%H J. Stauduhar, <a href="/A368161/a368161.txt">3772 known solutions</a>.

%e 128 + 144 + 169 = 441, and 441 is the first perfect power that is the sum of three consecutive perfect powers, so a(3) = 441.

%Y Cf. A001597.

%K sign,more

%O 1,2

%A _J. Stauduhar_ and _Tim Peters_, Dec 14 2023