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A373460 Numbers k such that k and k+1 both have an equal number of even and odd digits.

%I A373460 #14 Jun 07 2024 05:22:40
%S A373460 29,49,69,89,1009,1029,1049,1069,1089,1209,1229,1249,1269,1289,1409,
%T A373460 1429,1449,1469,1489,1609,1629,1649,1669,1689,1809,1829,1849,1869,
%U A373460 1889,2109,2129,2149,2169,2189,2309,2329,2349,2369,2389,2509,2529,2549,2569,2589,2709
%N A373460 Numbers k such that k and k+1 both have an equal number of even and odd digits.
%C A373460 The terms are of the form 100*m + j, where m is either 0 or a term of A227870 and j is in {29, 49, 69, 89} if m  = 0 or in {9, 29, 49, 69, 89} if m > 0.
%H A373460 Amiram Eldar, <a href="/A373460/b373460.txt">Table of n, a(n) for n = 1..10000</a>
%F A373460 a(n) = 100 * A227870(floor(n/5)) + 20 * (n mod 5) + 9, for n > 4.
%e A373460 29 is a term since it has one even digit (2) and one odd digit (9), and 29+1 = 30 also has one even digit (0) and one odd digit (3).
%t A373460 q[n_] := Module[{d = Differences[Tally[Mod[IntegerDigits[n], 2]]]}, d != {} && d[[1, 2]] == 0]; Select[Range[3000], q[#] && q[# + 1] &]
%o A373460 (PARI) iseq(n) = {my(o = 0, e = 0); while(n > 0, if((n%10) % 2 == 0, e++, o++); n \= 10); e == o;}
%o A373460 lista(kmax) = {my(q1 = 0, q2); for(k = 1, kmax, q2 = iseq(k); if(q1 && q2, print1(k-1, ", ")); q1 = q2);}
%Y A373460 Subsequence of A017377 and A227870.
%Y A373460 Cf. A337238 (binary analog), A373505.
%K A373460 nonn,base,easy
%O A373460 1,1
%A A373460 _Amiram Eldar_, Jun 07 2024