A030157 Even numbers k such that in k^2 the parity of digits alternates.

0, 2, 4, 6, 16, 26, 36, 74, 84, 96, 204, 264, 296, 384, 404, 426, 574, 584, 606, 726, 736, 764, 874, 884, 964, 1464, 1584, 1596, 1704, 2036, 2074, 2084, 2184, 2916, 2926, 2964, 3306, 3536, 3764, 3816, 4116, 4264, 4306, 5684, 5726, 5736, 5874

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 2000 terms from Robert Israel)

Crossrefs

Cf. A030158 (the squares).

Programs

Maple

alp:= proc(n) local L,d;
L:= convert(n,base,10);
d:= nops(L);
if d::even then L:= L + map(op, [[0,1]$(d/2)]) else L:= L + map(op, [[0,1]$((d-1)/2),[0]]) fi;
nops(convert(L mod 2, set))=1
end proc:
select(t -> alp(t^2), [seq(i,i=0..10000,2)]); # Robert Israel, Aug 15 2018

Mathematica

id[n_]:=IntegerDigits[n^2]; t={}; Do[If[Length[id[n]]==1, AppendTo[t, n], If[Union[Abs[Differences[Boole/@EvenQ[id[n]]]]]=={1}, AppendTo[t, n]]], {n, 0, 6000, 2}]; t (* Vincenzo Librandi, Aug 15 2018 *)
Join[{0,2},Select[Range[0,6000,2],Union[Abs[Differences[Boole[OddQ[ IntegerDigits[ #^2]]]]]] == {1}&]] (* Harvey P. Dale, Sep 11 2024 *)

Extensions

Offset changed by Robert Israel, Aug 15 2018