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A339715 Numbers with equal number of even and odd digits such that the product a(n) * a(n+1) has an equal number of even and odd digits too. 1
12, 92, 16, 67, 21, 49, 25, 41, 30, 38, 29, 43, 36, 47, 23, 61, 18, 72, 27, 54, 32, 58, 52, 34, 50, 65, 45, 63, 56, 70, 74, 14, 78, 69, 85, 90, 81, 76, 94, 87, 83, 96, 1047, 9562, 89, 1128, 98, 1036, 9667, 1041, 9618, 1058, 9461, 1061, 9432, 1074, 9340, 1083, 9243, 1087, 9205, 1090, 9203, 1100, 9201 (list; graph; refs; listen; history; text; internal format)
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) = 12 * 92 = 1104 (which has an equal number of even and odd digits);

a(2) * a(3) = 92 * 16 = 1472 (idem);

a(3) * a(4) = 16 * 67 = 1072 (idem);

a(4) * a(5) = 67 * 21 = 1407 (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 = [1], set()

  for n in range(1, nn+1):

    an = 12

    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(59))  # Michael S. Branicky, Dec 14 2020

CROSSREFS

Cf. A339714 (same idea, replacing multiplication by addition), A227870 (numbers with equal number of even and odd digits).

Sequence in context: A004311 A160869 A026074 * A298397 A246585 A120990

Adjacent sequences:  A339712 A339713 A339714 * A339716 A339717 A339718

KEYWORD

base,nonn

AUTHOR

Eric Angelini and Carole Dubois, Dec 14 2020

STATUS

approved

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)