A368161 a(n) = least perfect power m that is the sum of n consecutive perfect powers, or -1 if m does not exist.

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

Offset

1,2

Comments

It is conjectured that m always exists.

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

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

Known solutions < 10^12 from J. Stauduhar. All others from Tim Peters.

Links

Table of n, a(n) for n=1..8.

J. Stauduhar, 3772 known solutions.

Example

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

Crossrefs

Cf. A001597.

Sequence in context: A092430 A018207 A362428 * A264382 A337901 A260854

Adjacent sequences: A368158 A368159 A368160 * A368162 A368163 A368164

Keyword

sign,more

Author

J. Stauduhar and Tim Peters, Dec 14 2023

Status

approved