A298639 Numbers k such that the digital sum of k and the digital root of k have the same parity.

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, 27, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 60, 61, 62, 63, 70, 71, 72, 80, 81, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114

Offset: 1

Author

J. Stauduhar, Jan 26 2018

Keywords

• nonn
• easy
• base

Comments

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

Complement of A298638.

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

Links

• J. Stauduhar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

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 *)

PARI

dr(n)=if(n, (n-1)%9+1);
isok(n) = (sumdigits(n) % 2) == (dr(n) % 2); \\ Michel Marcus, Jan 26 2018

PARI

is(n)=bittest(sumdigits(n)-(n-1)%9,0)||!n \\ M. F. Hasler, Jan 26 2018

Python

#Digital sum of n.
def ds(n):
  if n < 10:
    return n
  return n % 10 + ds(n//10)
def A298639(term_count):
  seq = []
  m = 0
  n = 1
  while n <= term_count:
    s = ds(m)
    r = ((m - 1) % 9) + 1 if m else 0
    if s % 2 == r % 2:
      seq.append(m)
      n += 1
    m += 1
  return seq
print(A298639(100))