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A137119
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Numbers k such that k and k^2 use only the digits 2, 6, 7 and 9.
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0
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OFFSET
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1,1
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COMMENTS
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Generated with DrScheme.
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LINKS
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EXAMPLE
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269777^2 = 72779629729.
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MAPLE
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Extend:= proc(x, d)
local i;
op(select(t -> member(floor(t^2/10^(d)) mod 10, {2, 6, 7, 9}), [seq(i*10^d+x, i=[2, 6, 7, 9])]))
end proc:
R[0]:= {6, 7}:
for m from 1 to 10 do R[m]:= map(Extend, R[m-1], m) od:
{seq(op(select(t -> convert(convert(t^2, base, 10), set) subset {2, 6, 7, 9}, R[m])), m=0..10)}; # Robert Israel, Oct 04 2019
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PROG
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(Magma) [k:k in [1..10^6]| Set(Intseq(k)) join Set(Intseq(k^2)) subset {2, 6, 7, 9}]; // Marius A. Burtea, Oct 04 2019
(Python)
def test(n):
while n > 0:
d, n = n%10, n//10
if d == 0 or d == 1 or d == 3 or d == 4 or d == 5 or d == 8:
return 0
return 1
n, a = 0, 1
while n >= 0:
if test(a) and test(a*a):
n = n+1
print(n, a)
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008
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STATUS
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approved
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