A030477 Numbers k such that k^2 has property that all even digits occur together and all odd digits occur together.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 17, 18, 20, 21, 22, 24, 25, 28, 29, 30, 32, 34, 38, 40, 42, 44, 45, 47, 49, 51, 53, 56, 58, 60, 62, 65, 67, 68, 72, 76, 78, 79, 80, 83, 86, 88, 91, 92, 93, 98, 100, 102, 108, 118, 120, 122, 124, 132, 134, 138, 140

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A030476.

Programs

Maple

filter:= proc(n) local L,x,m;
  L:= convert(n^2,base,10) mod 2;
  if n::odd then
    if not member(0,L,m) then return true fi;
    convert(L[m..-1],set) = {0}
  else
    if not member(1,L,m) then return true fi;
    convert(L[m..-1],set) = {1}
  fi
end proc:
select(filter, [$0..1000]); # Robert Israel, Oct 27 2024

Python

def ok(n):
    s = "".join("0" if d in "02468" else "1" for d in str(n**2))
    return len(set(s.rstrip(s[-1]))) < 2
print([k for k in range(141) if ok(k)]) # Michael S. Branicky, Oct 27 2024