A298639 - OEIS

%I #33 Sep 25 2023 15:05:57

%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,

%T 27,30,31,32,33,34,35,36,40,41,42,43,44,45,50,51,52,53,54,60,61,62,63,

%U 70,71,72,80,81,90,100,101,102,103,104,105,106,107,108,110,111,112,113,114

%N Numbers k such that the digital sum of k and the digital root of k have the same parity.

%C Numbers k such that A113217(k) = A179081(k).

%C Complement of A298638.

%C Agrees with A039691 until a(65): A039691(65) = 109 is not in this sequence.

%H J. Stauduhar, <a href="/A298639/b298639.txt">Table of n, a(n) for n = 1..10000</a>

%t fQ[n_] := Mod[Plus @@ IntegerDigits@n, 2] == Mod[Mod[n -1, 9] +1, 2]; fQ[0] = True; Select[ Range[0, 104], fQ] (* _Robert G. Wilson v_, Jan 26 2018 *)

%o (Python)

%o #Digital sum of n.

%o def ds(n):

%o   if n < 10:

%o     return n

%o   return n % 10 + ds(n//10)

%o def A298639(term_count):

%o   seq = []

%o   m = 0

%o   n = 1

%o   while n <= term_count:

%o     s = ds(m)

%o     r = ((m - 1) % 9) + 1 if m else 0

%o     if s % 2 == r % 2:

%o       seq.append(m)

%o       n += 1

%o     m += 1

%o   return seq

%o print(A298639(100))

%o (PARI) dr(n)=if(n, (n-1)%9+1);

%o isok(n) = (sumdigits(n) % 2) == (dr(n) % 2); \\ _Michel Marcus_, Jan 26 2018

%o (PARI) is(n)=bittest(sumdigits(n)-(n-1)%9,0)||!n \\ _M. F. Hasler_, Jan 26 2018

%Y Cf. A007953, A010888, A113217, A179081, A298638, A039691.

%K nonn,easy,base

%O 1,3

%A _J. Stauduhar_, Jan 26 2018