[seqfan] (no subject)

c.zizka at email.cz c.zizka at email.cz
Mon Nov 9 16:42:16 CET 2009

Dear seqfans,

let a(n) is the difference between n-th triangular number and next perfect square (submitted to OEIS today).

a(n)= (ceiling(n*(n+1)/2))^2 - n*(n+1)/2

Interestingly a(n) takes values {0,1,3,4,6,8,9,10,13,15,16,19,21,22,...} and it seems no a(n) is from {2,5,7,11,12,14,17,18,20,23,...} .
In OEIS we can found for a(n)=0   A001108, for a(n)=1  A006451, for a(n)=3  A154138,  for a(n)=4  A154139 , for a(n)=6  A154140, for a(n)=8  A154141, for a(n)=9   A154142, for a(n)=10  A154143. 

Why can not be :

 (ceiling(n*(n+1)/2))^2  =  2+ n*(n+1)/2



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