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A225885
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Square numbers that remain square when their most-significant (or leftmost) digit is removed.
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10
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1, 4, 9, 49, 64, 81, 100, 225, 400, 625, 900, 1225, 2025, 3025, 4225, 4900, 5625, 6400, 7225, 8100, 9025, 10000, 15625, 22500, 27225, 30625, 34225, 40000, 42025, 50625, 60025, 62500, 70225, 75625, 81225, 90000, 93025, 105625, 122500, 202500, 275625, 302500, 330625
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OFFSET
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1,2
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COMMENTS
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The first three are the only terms not divisible by 25 (and thus, not ending in 00 or 25). If 100 is a term, then the sequence should start with 3 more initial terms, namely (1, 4, 9, ...) - M. F. Hasler, Nov 01 2014
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LINKS
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EXAMPLE
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225 = 15^2 becomes 25 = 5^2, 105625 = 325^2 becomes 5625 = 75^2.
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MATHEMATICA
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b^2 /. Flatten[Outer[Solve[a^2 + #2*10^#1 == b^2 && 0 <= a < Sqrt[10^#1] && Sqrt[#2*10^#1] <= b < Sqrt[10^(#1 + 1)], {a, b}, Integers] &, Range[0, 5], Range[9]], 2] (* Davin Park, Dec 30 2016 *)
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PROG
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(R)
no0<-function(s){ while(substr(s, 1, 1)=="0" & nchar(s)>1) s=substr(s, 2, nchar(s)); s};
issquare<-function(x) ifelse(as.bigz(x)<2, T, all(table(as.numeric(gmp::factorize(x)))%%2==0));
which(sapply(1:200, function(x) issquare(no0(substr(x^2, 2, ndig(x^2)))))>0)^2
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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