A114535 Numbers that can be represented as (m+1)^k - m^k in at least 3 ways, with k, m > 0.

1, 127, 3367, 14911

Offset

1,2

Comments

The decompositions for 1 are infinite and trivial, obtained letting k=1 and m arbitrary. The representations for the other entries are 127 = 64^2 - 63^2 = 7^3 - 6^3 = 2^7 - 1^7, 3367 = 1684^2 - 1683^2 = 34^3 - 33^3 = 4^6 - 3^6, 14911 = 7456^2 - 7455^2 = 71^3 - 70^3 = 16^4 - 15^4. Apparently there are no other solutions < 10^9.

Links

Table of n, a(n) for n=1..4.

Example

127 = 64^2 - 63^2 = 7^3 - 6^3 = 2^7 - 1^7.

Crossrefs

Cf. A115783.

Sequence in context: A345458 A008398 A144969 * A215611 A176357 A201071

Adjacent sequences: A114532 A114533 A114534 * A114536 A114537 A114538

Keyword

nonn,hard,more

Author

Giovanni Resta, Feb 15 2006

Status

approved