A242367 Numbers whose parity matches only their least significant decimal digit.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 21, 23, 25, 27, 29, 30, 32, 34, 36, 38, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 61, 63, 65, 67, 69, 70, 72, 74, 76, 78, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 110, 112, 114, 116, 118, 130, 132, 134, 136, 138

Offset

1,2

Comments

There are 9*5^(n-1) n-digit terms, hence a(n) << n^k with k = log 5/log 10 = 0.69897.... - Charles R Greathouse IV, May 12 2014

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

100 is not in the sequence since 100 is even but has 2 even digits (both the second and third digits).
998 is in the sequence since 998 is even and the only even digit is the final digit.

Maple

N:= 3: # for terms of up to N digits
fodd:= proc(t) local i; seq(10*t+i, i=1..9, 2) end proc:
feven:= proc(t) local i; seq(10*t+i, i=0..8, 2) end proc:
feven(0):= (2, 4, 6, 8):
A[0]:= [0]:
B[0]:= [0]:
for d from 1 to N-1 do
  A[d]:= map(feven, A[d-1]);
  B[d]:= map(fodd, B[d-1]);
od:
R:= NULL:
for i from 0 to N-1 do
  R:= R, op(map(fodd, A[i])),
   op(map(feven, B[i]))
od:
sort([R]); # Robert Israel, Sep 09 2024

Prog

(Python)
def ok(n): return set(str(n)[:-1]) & set(["02468", "13579"][n&1]) == set()
print([k for k in range(1, 140) if ok(k)]) # Michael S. Branicky, Sep 09 2024

Crossrefs

Sequence in context: A271168 A292514 A030141 * A355596 A246077 A064915

Adjacent sequences: A242364 A242365 A242366 * A242368 A242369 A242370

Keyword

nonn,base,look

Author

J. Lowell, May 12 2014

Status

approved