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

1,1

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

Table of n, a(n) for n=1..17.

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

Adjacent sequences: A137107 A137108 A137109 * A137111 A137112 A137113

Keyword

base,nonn,more,changed

Author

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

Status

approved