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

1,3

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

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 *)

Prog

(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))
(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

Crossrefs

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

Sequence in context: A295020 A298359 A039691 * A276347 A076121 A239427

Adjacent sequences: A298636 A298637 A298638 * A298640 A298641 A298642

Keyword

nonn,easy,base

Author

J. Stauduhar, Jan 26 2018

Status

approved