[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
:-)
Ctibor
p.s. sorry , now formula corrected
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