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A137110
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Numbers k such that k and k^2 use only the digits 2, 5, 6 and 7.
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5
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5, 25, 26, 75, 76, 275, 525, 526, 725, 7525, 27525, 72576, 256266, 276725, 725725, 276726675, 756652275
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OFFSET
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1,1
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COMMENTS
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Generated with DrScheme.
a(18) > 2*10^43 (if it exists).
If k = x*10^m is a term where 1 < x < 10 and k is not 25 or 76, then 2.5622756725665225652662672277265762225525525 < x < 7.5665565267667667557762552666757226626652626.
(End)
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LINKS
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EXAMPLE
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276726675^2 = 76577652656555625.
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PROG
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(Python)
def auptod(maxdigits, only="2567"):
aset, digset, valid = set(), set(only), set(only)
for e in range(1, maxdigits+1):
newvalid = set()
for tstr in valid:
t = int(tstr)
if set(str(t**2)) <= digset: aset.add(t)
for d in digset:
dtstr = d + tstr
dt = int(dtstr)
remstr = str(dt**2)[-e-1:]
if set(remstr) <= digset: newvalid.add(dtstr)
valid = newvalid
return sorted(aset)
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CROSSREFS
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KEYWORD
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base,nonn,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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