[seqfan] A property of numbers in A171640

Jean-Luc Manguin jean-luc.manguin at unicaen.fr
Tue Jun 2 16:51:34 CEST 2020


Hello, 

I would like to add a comment to the serie [ https://oeis.org/A171640 | A171640 ] 
But as I have 3 pending drafts I can't edit this sequence... 
Anyway I post it here. 
If a(n) is in A171240, then the number N = 6 x a(n) x (a(n) -1) is a square number. 
Moreover, if we consider the number P = 2 x (a(n) - 1) + sqrt(N) then : 

P x P + (P+1)x(P+1) + (P+2)x(P+2) = (P + a(n))x(P + a(n)) + (P + a(n) +1)x(P + a(n) +1) 

The first term a(1)=3 gives P=10 
and 10*10 + 11*11 + 12*12 = 13*13 + 14*14 = 365 

Thank you for your attention. 
Best regards. 

JL Manguin 



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