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

%I A358270 #48 Nov 12 2022 02:10:16
%S A358270 11,13,15,17,19,20,22,24,26,28,31,33,35,37,39,40,42,44,46,48,51,53,55,
%T A358270 57,59,60,62,64,66,68,71,73,75,77,79,80,82,84,86,88,91,93,95,97,99,
%U A358270 1001,1003,1005,1007,1009,1010,1012,1014,1016,1018,1021,1023,1025,1027,1029,1030
%N A358270 Numbers whose sum of digits is even and that have an even number of even digits.
%C A358270 There are only terms with an even number of digits, and precisely, there exist A137233(2*k) terms with 2*k digits.
%C A358270 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.
%C A358270 The opposite conditions, an odd sum of digits, and an odd number of odd digits, are the same and are A054684.
%F A358270 a(n) = t - A179081(t) where t = A001637(2*n). - _Kevin Ryde_, Nov 10 2022
%e A358270 26 is a term since 2+6 = 8 (even) and 26 has two even digits.
%e A358270 39 is a term since 3+9 = 12 (even) and 39 has zero even digits.
%e A358270 1012 is a term since 1+0+1+2 = 4 (even) and 1012 has two even digits.
%t A358270 Select[Range[1000], EvenQ[Plus @@ IntegerDigits[#]] && EvenQ[Plus @@ DigitCount[#, 10, Range[0, 8, 2]]] &] (* _Amiram Eldar_, Nov 06 2022 *)
%o A358270 (Python)
%o A358270 def ok(n): s = str(n); return sum(map(int, s))%2 == sum(1 for d in s if d in "02468")%2 == 0
%o A358270 print([k for k in range(1031) if ok(k)]) # _Michael S. Branicky_, Nov 06 2022
%o A358270 (Python)
%o A358270 from itertools import count, islice, chain
%o A358270 def A358270_gen(): # generator of terms
%o A358270     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))))
%o A358270 A358270_list = list(islice(A358270_gen(),61)) # _Chai Wah Wu_, Nov 11 2022
%o A358270 (PARI) a(n) = n*=2; n += 100^logint(110*n,100) \ 11; n - sumdigits(n)%2; \\ _Kevin Ryde_, Nov 10 2022
%Y A358270 Intersection of A054683 and A356929.
%Y A358270 Cf. A001637 (even length), A179081 (digit sum mod 2).
%Y A358270 Cf. A014263, A054684, A137233.
%K A358270 nonn,base,easy
%O A358270 1,1
%A A358270 _Bernard Schott_, Nov 06 2022