A136967 Numbers k such that k and k^2 use only the digits 1, 2, 3 and 4.

1, 2, 11, 12, 21, 111, 1111

Offset

1,2

Comments

Generated with DrScheme.

No further terms up to 444444444444. Conjecture: these are all the terms. - Robert Israel, Mar 01 2017

From Pontus von Brömssen, Apr 23 2024: (Start)

a(8) > 10^52 (if it exists).

If k = x*10^m is a term where 1 < x < 10 and k > 1111, then 1.1141114132411144244121413311312223343222114323114131 < x < 1.1141424242144423132424212124444121442241144431212312.

(End)

Links

Table of n, a(n) for n=1..7.

Jonathan Wellons, Tables of Shared Digits [archived].

Example

21^2 = 441, so 21 is a term.

Maple

dmax:= 8: # to get all terms of up to dmax digits
f:= proc(n) local L; L:= convert(n^2, base, 10); min(L) >= 1 and max(L) <= 4 end proc:
A:= NULL:
for d from 1 to dmax do
for i from 0 to 4^d-1 do
  R:= convert(i+4^d, base, 4);
  n:= add((R[i]+1)*10^(i-1), i=1..d);
  if filter(n) then A:= A, n fi
od
od:
A; # Robert Israel, Mar 01 2017

Prog

(PARI) isok(n) = {vno = [0, 5, 6, 7, 8, 9]; !#setintersect(Set(digits(n)), vno) && !#setintersect(Set(digits(n^2)), vno); } \\ Michel Marcus, Mar 01 2017

Crossrefs

Sequence in context: A089600 A114034 A136970 * A213975 A137001 A136996

Adjacent sequences: A136964 A136965 A136966 * A136968 A136969 A136970

Keyword

base,nonn,more

Author

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

Status

approved