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

1,2

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

Links

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

Index entries for 10-automatic sequences.

Example

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

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

Prog

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

Crossrefs

Cf. A061810, A276508.

Sequence in context: A328180 A218291 A062899 * A252066 A031101 A112423

Adjacent sequences: A061808 A061809 A061810 * A061812 A061813 A061814

Keyword

nonn,base,easy

Author

Amarnath Murthy, May 28 2001

Extensions

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

Offset corrected by Charles R Greathouse IV, Feb 15 2017

Status

approved