A358270 Numbers whose sum of digits is even and that have an even number of even digits.

11, 13, 15, 17, 19, 20, 22, 24, 26, 28, 31, 33, 35, 37, 39, 40, 42, 44, 46, 48, 51, 53, 55, 57, 59, 60, 62, 64, 66, 68, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 91, 93, 95, 97, 99, 1001, 1003, 1005, 1007, 1009, 1010, 1012, 1014, 1016, 1018, 1021, 1023, 1025, 1027, 1029, 1030

Offset

1,1

Comments

There are only terms with an even number of digits, and precisely, there exist A137233(2*k) terms with 2*k digits.

The conditions separately are A054683 for even sum of digits, and A356929 for even number of even digits, so that this sequence is their intersection.

The opposite conditions, an odd sum of digits, and an odd number of odd digits, are the same and are A054684.

Links

Table of n, a(n) for n=1..61.

Formula

a(n) = t - A179081(t) where t = A001637(2*n). - Kevin Ryde, Nov 10 2022

Example

26 is a term since 2+6 = 8 (even) and 26 has two even digits.
39 is a term since 3+9 = 12 (even) and 39 has zero even digits.
1012 is a term since 1+0+1+2 = 4 (even) and 1012 has two even digits.

Mathematica

Select[Range[1000], EvenQ[Plus @@ IntegerDigits[#]] && EvenQ[Plus @@ DigitCount[#, 10, Range[0, 8, 2]]] &] (* Amiram Eldar, Nov 06 2022 *)

Prog

(Python)
def ok(n): s = str(n); return sum(map(int, s))%2 == sum(1 for d in s if d in "02468")%2 == 0
print([k for k in range(1031) if ok(k)]) # Michael S. Branicky, Nov 06 2022
(Python)
from itertools import count, islice, chain
def A358270_gen(): # generator of terms
    return filter(lambda n:not (len(s:=str(n))&1 or sum(int(d) for d in s)&1), chain.from_iterable((range(10**l, 10**(l+1)) for l in count(1, 2))))
A358270_list = list(islice(A358270_gen(), 61)) # Chai Wah Wu, Nov 11 2022
(PARI) a(n) = n*=2; n += 100^logint(110*n, 100) \ 11; n - sumdigits(n)%2; \\ Kevin Ryde, Nov 10 2022

Crossrefs

Intersection of A054683 and A356929.

Cf. A001637 (even length), A179081 (digit sum mod 2).

Cf. A014263, A054684, A137233.

Sequence in context: A163140 A048596 A228709 * A358076 A292513 A171491

Adjacent sequences: A358267 A358268 A358269 * A358271 A358272 A358273

Keyword

nonn,base,easy

Author

Bernard Schott, Nov 06 2022

Status

approved