A272615 Numbers with digits in descending numerical order in base 2, 3 and 4 expansions.

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

Offset: 1

Author

Robin Powell, May 03 2016

Keywords

• nonn
• base

Comments

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

Examples

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

Crossrefs

Intersection of A023758, A023759, and A023760.

Programs

PARI

dec(n,b)=my(v=digits(n,b)); v==vecsort(v,,4)
is(n)=dec(n,2) && dec(n,3) && dec(n,4) \\ Charles R Greathouse IV, May 03 2016

PARI

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