[seqfan] (no subject)

c.zizka at email.cz c.zizka at email.cz
Mon Nov 9 16:46:17 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(sqrt(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(sqrt(n*(n+1)/2)))^2  =  2+ n*(n+1)/2

p.s. sorry , now formula corrected

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