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A137110
Numbers k such that k and k^2 use only the digits 2, 5, 6 and 7.
5
5, 25, 26, 75, 76, 275, 525, 526, 725, 7525, 27525, 72576, 256266, 276725, 725725, 276726675, 756652275
OFFSET
1,1
COMMENTS
Generated with DrScheme.
If it exists, a(18) > 10^34. - David A. Corneth and Michael S. Branicky, May 25 2021
From Pontus von Brömssen, May 01 2024: (Start)
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)
LINKS
David A. Corneth, PARI program
Jonathan Wellons, Tables of Shared Digits [archived].
EXAMPLE
276726675^2 = 76577652656555625.
PROG
(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)
print(auptod(16)) # Michael S. Branicky, May 25 2021
(PARI) \\ See PARI link. David A. Corneth, May 25 2021
CROSSREFS
Sequence in context: A070381 A136912 A137111 * A036137 A070380 A068574
KEYWORD
base,nonn,more
AUTHOR
Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008
STATUS
approved