A298638 Numbers k such that the digital sum of k and the digital root of k have opposite parity.

19, 28, 29, 37, 38, 39, 46, 47, 48, 49, 55, 56, 57, 58, 59, 64, 65, 66, 67, 68, 69, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 109, 118, 119, 127, 128, 129, 136, 137, 138, 139, 145, 146, 147, 148, 149, 154, 155

Offset: 1

Author

J. Stauduhar, Jan 23 2018

Keywords

• nonn
• easy
• base

Comments

Numbers k such that A113217(k) <> A179081(k).

Complement of A298639.

Agrees with A291884 until a(46): a(46) = 109 is not in that sequence.

Links

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

Crossrefs

Cf. A007953, A010888, A113217, A179081.

Cf. A298639, A291884.

Programs

Mathematica

Select[Range[145], EvenQ@ Total@ IntegerDigits@ # != EvenQ@ NestWhile[Total@ IntegerDigits@ # &, #, # > 9 &] &] (* Michael De Vlieger, Feb 03 2018 *)

PARI

isok(n) = sumdigits(n) % 2 != if (n, ((n-1)%9+1) % 2, 0); \\ Michel Marcus, Mar 01 2018

Python

#Digital sum of n.
def ds(n):
  if n < 10:
    return n
  return n % 10 + ds(n//10)
def A298638(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(A298638(100))