A137119 Numbers k such that k and k^2 use only the digits 2, 6, 7 and 9.

26, 27, 277, 269777

Offset

1,1

Comments

Generated with DrScheme.

No further terms up to 2*10^27. - Robert Israel, Oct 04 2019

From Pontus von Brömssen, May 01 2024: (Start)

a(5) > 2*10^48 (if it exists).

If k = x*10^m is a term where 1 < x < 10 and k is not 26, then 2.696779972972726222722227692792927222296799669262 < x < 9.629629779996726296779967279792972729927676699723.

(End)

Links

Table of n, a(n) for n=1..4.

J. Wellons, Tables of Shared Digits

Example

269777^2 = 72779629729.

Maple

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

Prog

(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)
    a = a+1 # A.H.M. Smeets, Oct 05 2019

Crossrefs

Sequence in context: A136923 A042394 A137118 * A042396 A042398 A042400

Adjacent sequences: A137116 A137117 A137118 * A137120 A137121 A137122

Keyword

nonn,base,more

Author

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

Status

approved