A137110 Numbers k such that k and k^2 use only the digits 2, 5, 6 and 7.

5, 25, 26, 75, 76, 275, 525, 526, 725, 7525, 27525, 72576, 256266, 276725, 725725, 276726675, 756652275

Offset: 1

Author

Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Keywords

• base
• nonn
• more

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)

Examples

			276726675^2 = 76577652656555625.
		

Links

• David A. Corneth, PARI program
• Jonathan Wellons, Tables of Shared Digits [archived].

Programs

PARI

\\ See PARI link. David A. Corneth, May 25 2021

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