A293695 Numbers z such that x^2 + y^8 = z^2 (with positive integers x and y) and gcd(x, y, z) = 1.

65, 3281, 6625, 16385, 22945, 195313, 198593, 390689, 407009, 419905, 810529, 2882401, 2885681, 3077713, 4194305, 4200865, 4584929, 5764865, 5781185, 6184705, 9959105, 21523361, 21718673, 24405761, 25000001, 25006561, 30764801, 43046785, 43063105, 47241025

Offset

1,1

Comments

Subsequence of A293694.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

63^2 + 2^8 = 65^2 and gcd(63, 2, 65) = 1, 65 is a term.
24999999^2 + 10^8 = 25000001^2 and gcd(24999999, 10, 25000001) = 1, 25000001 is a term.

Mathematica

z={}; Do[If[IntegerQ[(n^2 - y^8)^(1/2)] && GCD[y, n]==1, AppendTo[z, n]], {n, 5.1*10^7}, {y, (n^2 - 1)^(1/8)}]; z

Crossrefs

Cf. A293284, A293691, A293693, A293694.

Sequence in context: A075474 A069225 A211960 * A133853 A188693 A206876

Adjacent sequences: A293692 A293693 A293694 * A293696 A293697 A293698

Keyword

nonn

Author

XU Pingya, Oct 16 2017

Status

approved