A273753 Taxi-cab numbers (A001235) that are the average of two positive cubes in more than one way.

6742008, 53936064, 182034216, 431488512, 842751000, 1456273728, 1581292125, 2312508744, 3451908096, 4914923832, 6742008000, 8973612648, 11395366632, 11650189824, 12650337000, 14812191576, 18500069952, 22754277000, 27615264768, 33123485304, 39319390656

Offset: 1

Author

Altug Alkan, May 29 2016

Keywords

• nonn

Comments

Motivation for this sequence is that question: What is the least odd term of this sequence?

1581292125 = 3^6*5^3*7*37*67 is the least odd number that is the term of this sequence.

Examples

			6742008 is a term because 6742008 = 46^3 + 188^3 = 126^3 + 168^3 = (14^3 + 238^3)/2 = (105^3 + 231^3)/2.
53936064 is a term because 53936064 = 2^3*6742008.
1581292125 is a term because 1581292125 = 50^3 + 1165^3 = 540^3 + 1125^3 = (435^3 + 1455^3)/2 = (909^3 + 1341^3)/2.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..64

Crossrefs

Cf. A001235, A191345.

Programs

PARI

T = thueinit(x^3+1, 1);
isA001235(n) = my(v=thue(T, n)); sum(i=1, #v, v[i][1]>=0 && v[i][2]>=v[i][1])>1;
isok(n) = isA001235(n) && isA001235(2*n);

Extensions

a(5)-a(21) from Giovanni Resta, Jun 01 2016