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A030476
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Squares with property that all even digits occur together and all odd digits occur together.
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3
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0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 144, 196, 225, 289, 324, 400, 441, 484, 576, 625, 784, 841, 900, 1024, 1156, 1444, 1600, 1764, 1936, 2025, 2209, 2401, 2601, 2809, 3136, 3364, 3600, 3844, 4225, 4489, 4624, 5184, 5776, 6084, 6241, 6400
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OFFSET
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0,3
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COMMENTS
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Among first 22083 terms (up to 10^14), there are 19202 even and 2881 odd terms. Also note that in odd terms, the only odd digit is the last one. - Zak Seidov, Apr 17 2016
For any k>=1, (10^k-2)^2 is a member of the sequence with the first k-1 digits odd and the last k+1 even, while (2*10^k+2)^2 = 4*10^(2*k)+8*10^k+4 is a member with all digits even, and (2*10^k+1)^2 is an odd member.
If x is an even member, then so is 100*x. (End)
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LINKS
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EXAMPLE
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a(21054)=9427771^2=88882866028441, - Zak Seidov, Apr 18 2016
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MAPLE
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filter:= proc(n) local L, evens, odds;
L:= convert(n, base, 10) mod 2;
evens:= select(t -> L[t]::even, [$1..nops(L)]);
odds:= select(t -> L[t]::odd, [$1..nops(L)]);
(evens = []) or (odds = []) or (evens[1]>odds[-1]) or (odds[1]>evens[-1])
end proc:
select(filter, [seq(i^2, i=0..100)]); # Robert Israel, Apr 18 2016
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MATHEMATICA
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Select[Range[0, 80]^2, Function[k, Or[Flatten@ # == k, Flatten@ Reverse@ # == k] &@ GatherBy[k, EvenQ]]@ IntegerDigits@ # &] (* Michael De Vlieger, Apr 17 2016 *)
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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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STATUS
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approved
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