[seqfan] Re: n = 562576374032409

[Vladimir Shevelev]

Dear Zak and SeqFans,

I only want to notice that
we have the following pairs
n, n+1 that both represented
as sum of two cubes: for t>=1,

n=(2t^2-t-1)^3+(2t^2+t-1)^3, 

n+1=(2t^2-1)^3+(2t^2)^3.

Your case is obtained for t=181.
Now we should try to choose t
such that n to be a taxi-cab number.

Best regards,
Vladimir

________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Zak Seidov via SeqFan [seqfan at list.seqfan.eu]
Sent: 26 May 2016 20:13
To: math-fun; Sequence Fanatics Discussion list
Cc: Zak Seidov
Subject: [seqfan] n = 562576374032409

 Integer n = 562576374032409 is unique in the sense that
n and n+1 are sums of two cubes:
n = 60684^3 + 69734^3, n+1 = 65521^3 + 65522^3
and also n is the taxi-cab number:
n = 60684^3 + 69734^3 = 65340^3 + 65702^3.
Is n the least such number?
Are there larger such numbers?
Zak

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