A061811 Multiples of 3 with all even digits.

0, 6, 24, 42, 48, 60, 66, 84, 204, 222, 228, 240, 246, 264, 282, 288, 402, 408, 420, 426, 444, 462, 468, 480, 486, 600, 606, 624, 642, 648, 660, 666, 684, 804, 822, 828, 840, 846, 864, 882, 888, 2004, 2022, 2028, 2040, 2046, 2064, 2082, 2088, 2202, 2208

Offset: 1

Author

Amarnath Murthy, May 28 2001

Keywords

• nonn
• base
• easy

Comments

The numbers b(d) of terms from 10^(d-1) to 10^d satisfy the recurrence b(d) = 6 b(d-1) - 6 b(d-2) + 5 b(d-3) with b(1)=1, b(2)=6, b(3)=33. For d >= 4, b(d) = (3*A276508(d) - 10*A276508(d-1) + 3*A276508(d-2))/7. - Robert Israel, Feb 15 2017

Examples

			228 has all even digits and 228 = 3*76.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Index entries for 10-automatic sequences.

Crossrefs

Cf. A061810, A276508.

Programs

Maple

N:= 4: # for all terms < 10^N
E[1,0]:= {6}:
E[1,1]:= {4}:
E[1,2]:= {2,8}:
for n from 2 to N do
  for j from 0 to 2 do
    E[n,j]:= map(t -> (10*t, 10*t+6),E[n-1,j]) union
             map(t -> (10*t+2, 10*t+8), E[n-1,j+1 mod 3]) union
           map(t -> 10*t+4, E[n-1,j+2 mod 3]);
od od:
A:=sort([0,seq(op(E[i,0]),i=1..N)]); # Robert Israel, Feb 15 2017

Mathematica

Select[3*Range[0,800],AllTrue[IntegerDigits[#],EvenQ]&] (* Harvey P. Dale, May 03 2025 *)

PARI

is(n)=n%3==0 && #setintersect(Set(digits(n)), [1,3,5,7,9])==0 \\ Charles R Greathouse IV, Feb 15 2017

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 30 2001

Offset corrected by Charles R Greathouse IV, Feb 15 2017