A251853 Nonnegative numbers n with all even digits such that the digital sum of the digits' sum is even.

0, 2, 4, 6, 8, 20, 22, 24, 26, 40, 42, 44, 60, 62, 80, 200, 202, 204, 206, 220, 222, 224, 240, 242, 260, 400, 402, 404, 420, 422, 440, 488, 600, 602, 620, 668, 686, 688, 800, 848, 866, 868, 884, 886, 888, 2000, 2002, 2004, 2006, 2020, 2022, 2024, 2040, 2042, 2060, 2200

Offset

1,2

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

Each digit in n is divisible by two, n is divisible by 2, the sum S of the digits of n is divisible by 2, and the sum of the digits of S is also divisible by 2.

Example

2288 is in the sequence because it is even, 2 and 8 are even, 2 + 2 + 8 + 8 = 20 is even, and 2 + 0 = 2 is even.

Mathematica

a251853[n_Integer] := Module[{digitSum}, digitSum[x_] := Plus @@ IntegerDigits[x]; Select[Range[n], And[And @@ EvenQ@IntegerDigits[#], EvenQ@digitSum[#], EvenQ@Nest[digitSum, #, 2]] &]]; a251853[2200] (* Michael De Vlieger, Dec 11 2014 *)

Prog

(PARI) isevend(v) = for (i=1, #v, if (v[i] % 2, return (0))); return (1);
isok(n) = isevend(digits(n)) && ((sumdigits(sumdigits(n)) % 2) == 0); \\ Michel Marcus, Dec 11 2014
(Sage)
[x for x in [0..2200] if prod([is_even(i) for i in x.digits()]) and sum(Integer(sum(x.digits())).digits())%2==0] # Tom Edgar, Dec 10 2014
(Python)
A251853_list = [int(''.join(d)) for d in product('02468', repeat=4) if not sum(int(y) for y in str(sum(int(x) for x in d))) % 2] # Chai Wah Wu, Dec 20 2014

Crossrefs

Cf. A007953, A014263, A054683.

Sequence in context: A062897 A014263 A169906 * A061651 A350538 A131122

Adjacent sequences: A251850 A251851 A251852 * A251854 A251855 A251856

Keyword

nonn,base

Author

Chase Fortier, Dec 09 2014

Status

approved