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Numbers k such that k^2 contains only digits {0,2,5}, not ending with zero.
2

%I #42 Apr 04 2024 10:41:50

%S 5,15,45,235,505,745,1415,1485,4495,5005,15985,50005,72495,469255,

%T 500005,500505,1597505,1598515,4474955,5000005,5000505,5050005,

%U 7085235,15008515,44949995,50000005,50000505,50005005,50500005,500000005,500000505

%N Numbers k such that k^2 contains only digits {0,2,5}, not ending with zero.

%C Most terms have a special pattern in that they have only digits 0 and 5 and could be written as Sum_{h=0..t} 5*10^f(h), where 2f(h), 2f(h)-1, and f(h1) + f(h2) are all distinct and f(0)=0 for the nonzero ending constraint. - _Zhao Hui Du_, Mar 12 2024

%H Zhao Hui Du, <a href="/A058425/b058425.txt">Table of n, a(n) for n = 1..5913</a>

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/threedigits.htm">Index to related sequences</a>.

%H Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/math02/math0210.htm#025">Sporadic tridigital solutions</a>.

%Y Cf. A058426.

%K nonn,base

%O 1,1

%A _Patrick De Geest_, Nov 15 2000

%E a(29)=50500005 inserted by _Georg Fischer_, Jan 12 2022