A339714 Numbers with equal number of even and odd digits such that the sum a(n) + a(n+1) has an equal number of even and odd digits too.

10, 1090, 12, 18, 14, 16, 25, 27, 23, 29, 21, 49, 32, 38, 34, 36, 45, 47, 43, 1007, 54, 1009, 41, 1029, 52, 1018, 56, 1005, 58, 1003, 67, 1014, 69, 1001, 89, 1120, 81, 1021, 83, 1023, 85, 1041, 61, 1043, 63, 1027, 65, 1016, 74, 1030, 70, 1032, 72, 1034, 90, 1010, 92, 1012, 78, 1050, 50, 1052, 76, 1070, 30

Offset

1,1

Comments

Lexicographically earliest sequence of distinct positive terms with this property.

Numbers with an odd digit length cannot be in this sequence.

Links

Table of n, a(n) for n=1..65.

Example

a(1) + a(2) = 10 + 1090 = 1100 (which has an equal number of even and odd digits);
a(2) + a(3) = 1090 + 12 = 1102 (idem);
a(3) + a(4) = 12 + 18 = 30 (idem);
a(4) + a(5) = 18 + 14 = 32 (idem); etc.

Prog

(Python)
def cond(i):
  stri = str(i)
  se = sum(1 for d in stri if d in "02468")
  so = sum(1 for d in stri if d in "13579")
  return se == so
def aupto(nn):
  alst, used = [0], set()
  for n in range(1, nn+1):
    an = 10
    while True:
      while an in used: an += 1
      if cond(an) and cond(an + alst[-1]):
        alst.append(an); used.add(an); break
      an += 1
  return alst[1:] # use alst[n] for a(n)
print(aupto(56))  # Michael S. Branicky, Dec 14 2020

Crossrefs

Cf. A339715 (same idea, replacing addition by multiplication), A227870 (numbers with equal number of even and odd digits).

Sequence in context: A226553 A054609 A119045 * A069886 A133383 A268229

Adjacent sequences: A339711 A339712 A339713 * A339715 A339716 A339717

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Dec 14 2020

Status

approved