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Numbers with digits in descending numerical order in base 2, 3 and 4 expansions.
1

%I #10 May 03 2016 17:04:54

%S 0,1,2,3,4,8,12,63,240

%N Numbers with digits in descending numerical order in base 2, 3 and 4 expansions.

%C a(10), if it exists, has more than 1000 decimal digits. Conjecture: there are no more terms in this sequence. - _Charles R Greathouse IV_, May 03 2016

%e 12 is 1100 in base 2, 110 in base 3 and 30 in base 4; in each representation every digit is smaller than or equal to the one proceeding so 12 is a term.

%e Similarly, 63 is 111111 in base 2, 2100 in base 3 and 333 in base 4 so it is also a term.

%o (PARI) dec(n,b)=my(v=digits(n,b)); v==vecsort(v,,4)

%o is(n)=dec(n,2) && dec(n,3) && dec(n,4) \\ _Charles R Greathouse IV_, May 03 2016

%o (PARI) dec(n,b)=my(v=digits(n,b)); v==vecsort(v,,4)

%o list(lim)=my(v=List([0]),t); for(i=1,logint(lim\1+1,4), t=4^i-1; while(t<=lim, if(dec(t,3), listput(v,t)); t*=4); t=2*4^i-2; while(t<=lim, if(dec(t,3), listput(v,t)); t*=4)); Set(v) \\ _Charles R Greathouse IV_, May 03 2016

%Y Intersection of A023758, A023759, and A023760.

%K nonn,base

%O 1,3

%A _Robin Powell_, May 03 2016