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

1,3

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

Links

Table of n, a(n) for n=1..9.

Example

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.

Prog

(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

Crossrefs

Intersection of A023758, A023759, and A023760.

Sequence in context: A057608 A060984 A226947 * A356188 A238962 A238975

Adjacent sequences: A272612 A272613 A272614 * A272616 A272617 A272618

Keyword

nonn,base

Author

Robin Powell, May 03 2016

Status

approved