# [seqfan] Re: Subset of A152824

Robert Israel israel at math.ubc.ca
Sun Dec 14 08:11:02 CET 2008

```
On Sat, 13 Dec 2008, zak seidov wrote:

> %I A152834
> %S A152834 223,2233,2323,3223,22333,23233,23323,32233,32323,33223,222223,223333,
> %T A152834 232333,233233,233323,322333,323233,323323,332233,332323,333223
> %N A152834 Numbers of form 6k+1 that use only digits 2 and 3.
> %t A152834 Do[If[Union[IntegerDigits[6k+1]]=={2,3},Print[6k+1]],{k,100000}]
> %Y A152834 Subset of A152824.
> %K A152834 nonn
> %O A152834 1,1
> %A A152834 Zak Seidov (zakseidov(AT)yahoo.com), Dec 14 2008
>

In Maple, a faster way, producing all 340 terms < 10^10:

> M:= proc(n) option remember; (map(t -> 2*10^n+t,M(n-1)) union map(t ->
3*10^n+t,M(n-1))) end proc;
M(0):= {2,3};
select(t -> (t mod 6 = 1), `union`(seq(M(n),n=1..9)));

{223, 2233, 2323, 3223, 22333, 23233, 23323, 32233, 32323, 33223, 222223,
223333, 232333, 233233, 233323, 322333, 323233, 323323, 332233, 332323,
333223, 2222233, 2222323, 2223223, 2232223, 2233333, 2322223, 2323333,
2332333, 2333233, 2333323, 3222223, 3223333, 3232333, 3233233, 3233323,
3322333, 3323233, 3323323, 3332233, 3332323, 3333223, 22222333, 22223233,
22223323, 22232233, 22232323, 22233223, 22322233, 22322323, 22323223,
22332223, 22333333, 23222233, 23222323, 23223223, 23232223, 23233333,
23322223, 23323333, 23332333, 23333233, 23333323, 32222233, 32222323,
32223223, 32232223, 32233333, 32322223, 32323333, 32332333, 32333233,
32333323, 33222223, 33223333, 33232333, 33233233, 33233323, 33322333,
33323233, 33323323, 33332233, 33332323, 33333223, 222222223, 222223333,
222232333, 222233233, 222233323, 222322333, 222323233, 222323323,
222332233, 222332323, 222333223, 223222333, 223223233, 223223323,
223232233, 223232323, 223233223, 223322233, 223322323, 223323223,
223332223, 223333333, 232222333, 232223233, 232223323, 232232233,
232232323, 232233223, 232322233, 232322323, 232323223, 232332223,
232333333, 233222233, 233222323, 233223223, 233232223, 233233333,
233322223, 233323333, 233332333, 233333233, 233333323, 322222333,
322223233, 322223323, 322232233, 322232323, 322233223, 322322233,
322322323, 322323223, 322332223, 322333333, 323222233, 323222323,
323223223, 323232223, 323233333, 323322223, 323323333, 323332333,
323333233, 323333323, 332222233, 332222323, 332223223, 332232223,
332233333, 332322223, 332323333, 332332333, 332333233, 332333323,
333222223, 333223333, 333232333, 333233233, 333233323, 333322333,
333323233, 333323323, 333332233, 333332323, 333333223, 2222222233,
2222222323, 2222223223, 2222232223, 2222233333, 2222322223, 2222323333,
2222332333, 2222333233, 2222333323, 2223222223, 2223223333, 2223232333,
2223233233, 2223233323, 2223322333, 2223323233, 2223323323, 2223332233,
2223332323, 2223333223, 2232222223, 2232223333, 2232232333, 2232233233,
2232233323, 2232322333, 2232323233, 2232323323, 2232332233, 2232332323,
2232333223, 2233222333, 2233223233, 2233223323, 2233232233, 2233232323,
2233233223, 2233322233, 2233322323, 2233323223, 2233332223, 2233333333,
2322222223, 2322223333, 2322232333, 2322233233, 2322233323, 2322322333,
2322323233, 2322323323, 2322332233, 2322332323, 2322333223, 2323222333,
2323223233, 2323223323, 2323232233, 2323232323, 2323233223, 2323322233,
2323322323, 2323323223, 2323332223, 2323333333, 2332222333, 2332223233,
2332223323, 2332232233, 2332232323, 2332233223, 2332322233, 2332322323,
2332323223, 2332332223, 2332333333, 2333222233, 2333222323, 2333223223,
2333232223, 2333233333, 2333322223, 2333323333, 2333332333, 2333333233,
2333333323, 3222222223, 3222223333, 3222232333, 3222233233, 3222233323,
3222322333, 3222323233, 3222323323, 3222332233, 3222332323, 3222333223,
3223222333, 3223223233, 3223223323, 3223232233, 3223232323, 3223233223,
3223322233, 3223322323, 3223323223, 3223332223, 3223333333, 3232222333,
3232223233, 3232223323, 3232232233, 3232232323, 3232233223, 3232322233,
3232322323, 3232323223, 3232332223, 3232333333, 3233222233, 3233222323,
3233223223, 3233232223, 3233233333, 3233322223, 3233323333, 3233332333,
3233333233, 3233333323, 3322222333, 3322223233, 3322223323, 3322232233,
3322232323, 3322233223, 3322322233, 3322322323, 3322323223, 3322332223,
3322333333, 3323222233, 3323222323, 3323223223, 3323232223, 3323233333,
3323322223, 3323323333, 3323332333, 3323333233, 3323333323, 3332222233,
3332222323, 3332223223, 3332232223, 3332233333, 3332322223, 3332323333,
3332332333, 3332333233, 3332333323, 3333222223, 3333223333, 3333232333,
3333233233, 3333233323, 3333322333, 3333323233, 3333323323, 3333332233,
3333332323, 3333333223}

Cheers,
Robert Israel

```