A274367 Taxi-cab numbers (A001235) that are of the form x^2 + y^4 in more than one way (x, y > 0).

27445392, 1644443281, 2367885312, 5687433577, 112416325632, 208265121792, 900069054976, 1976398601697, 6735639678976, 9698858237952, 9911785815477, 14585606569872, 15283760730112, 18156501172017, 23295727931392, 29871321586561, 33510832422912, 67250060669952

Offset: 1

Author

Altug Alkan, Jun 19 2016

Keywords

• nonn

Comments

A272701(3) = 27445392 is the least number with the property that sequence focuses on.

If n = a^3 + b^3 = c^3 + d^3 = x^2 + y^4 = z^2 + t^4, then n*k^12 = (a*k^4)^3 + (b*k^4)^3 = (c*k^4)^3 + (d*k^4)^3 = (x*k^6)^2 + (y*k^3)^4 = (z*k^6)^2 + (t*k^3)^4. So if n is this sequence, then n*k^12 is also in this sequence for all k > 1.

Examples

			27445392 is a term because 27445392 = 141^3 + 291^3 = 198^3 + 270^3 = 756^2 + 72^4 = 5076^2 + 36^4.
112416325632 is a term because 112416325632 = 27445392*2^12.
		

Crossrefs

Cf. A001235, A111925, A272701.

Extensions

a(2)-a(18) from Giovanni Resta, Jun 19 2016