A292872 Perfect n-th powers y^n (n >= 3) of the form x^2 + 2^a * 11^b (x >= 1, a, b >= 0, gcd(x, y) = 1).

27, 81, 125, 243, 729, 3375, 15625, 59049, 704969, 33698267, 41063625, 86938307, 100544625, 483736625, 163218919625

Offset

1,1

Comments

Cangul, Demirci, Luca, Pinter and Soydan showed that there are no other terms.

Links

Table of n, a(n) for n=1..15.

I. N. Cangul, M. Demirci, F. Luca, A. Pinter and G. Soydan, On the Diophantine Equation x^2 + 2^a 11^b = y^n, Fibonacci Quart. 48 (2010), 39-46.

Example

a(8) = 59049 = 241^2 + 2^3 * 11^2 = 3^10 = 9^5

Crossrefs

Cf. A295233 (2^a * 5^b instead of 2^a * 11^b).

Sequence in context: A129254 A215782 A216438 * A057609 A255624 A008884

Adjacent sequences: A292869 A292870 A292871 * A292873 A292874 A292875

Keyword

nonn,fini,full

Author

Tomohiro Yamada, Nov 19 2017

Status

approved