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<TITLE>Scaled Chebyshev U-polynomials evaluated at sqrt(3)/2</TITLE>
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<DIV>Dear SeqFans,</DIV>
<DIV>just submitted A106265 (see below). </DIV>
<DIV> </DIV>
<DIV>My request to SEQGurus:</DIV>
<DIV>Are there missing numbers? <BR>Is it
known/correct/interesting...?</DIV>
<DIV>Thanks,</DIV>
<DIV>Zak</DIV>
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<DIV><FONT size=2><BR>%I A106265<BR>%S A106265
2,4,7,11,13,15,18,19,20,23,25,26,28,35,39,40,44,45,47,48,49,53,54,55,56,60<BR>%N
A106265 Numbers a such that equation Diophantine a+b^2=c^3 has integer
solution(s) b and c.<BR>%C A106265 Relative (minimal) values of b and c:
A106266,
A106267:<BR>b=5,2,1,4,70,7,3,18,14,2,10,1,6,36,5,52,9,96,13,4,524,26,17,3,76,2<BR>c=3,2,2,3,17,4,3,
7, 6,3, 5,3,4,11,4,14,5,21, 6,4, 65, 9, 7,4,18,4<BR>Cf. A023055:
(Apparently) differences between adjacent perfect powers <BR>(integers of
form a^b, a >= 1, b >= 2;<BR>A076438: n which appear to have a unique
representation as the difference <BR>of two perfect powers; that is, there
is only one solution <BR>to Pillai's equation a^x - b^y = n, with a>0,
b>0, x>1, y>1;<BR>A076440: n which appear to have a unique
representation as <BR>the difference of two perfect powers and one of those
powers is odd; <BR>that is, there is only one solution to Pillai's equation
a^x - b^y = n, <BR>with a>0, b>0, x>1, y>1, <BR>and that
solution has odd x or odd y (or both odd); <BR>A075772: Difference between
n-th perfect power and the closest perfect power, etc.<BR>%F A106265
A106265(n) = [A106267(n)]^3-[A106266(n)]^2<BR>%Y A106265
A023055,A075772,A076438,A076440,A106266,A106267.<BR>%O A106265 1<BR>%K
A106265 ,hard,more,nonn,unkn,<BR>%A A106265 Zak Seidov
(zakseidov@yahoo.com), Apr 28 2005<BR></FONT><FONT
size=2><BR></DIV></FONT></BLOCKQUOTE></BLOCKQUOTE>
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