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

1,1

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.

Links

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

Example

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.

Prog

(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);

Crossrefs

Cf. A001235, A191345.

Sequence in context: A234711 A309385 A022237 * A116173 A345608 A346282

Adjacent sequences: A273750 A273751 A273752 * A273754 A273755 A273756

Keyword

nonn

Author

Altug Alkan, May 29 2016

Extensions

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

Status

approved