A044821 Positive integers having distinct base-10 run lengths.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 133, 144, 155, 166, 177, 188, 199, 200, 211, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 233, 244, 255

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Examples

			117 is in the sequence because it has a run length of 2 and a run length of 1. 101 is not in the sequence because it has three run lengths of 1. - _R. J. Mathar_, Jan 18 2018
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A044813, A044814, A044815, A044816, A044817, A044818, A044819, A044820, A044821, A044822, A044823, A044824, A044825, A044826, A044827 (base 2 to base 16).

Programs

Maple

rlset := proc(L::list)
    local lset,rl,i ;
    lset := [] ;
    rl := 1 ;
    for i from 2 to nops(L) do
        if op(i,L) = op(i-1,L) then
            rl := rl+1 ;
        else
            lset := [op(lset),rl] ;
            rl := 1;
        end if;
    end do:
    lset := [op(lset),rl] ;
end proc:
isA044821 := proc(n)
    local dgs,rl;
    dgs := convert(n,base,10) ;
    rl := rlset(dgs) ;
    if nops(rl) = nops( convert(rl,set)) then
        true;
    else
        false;
    end if;
end proc:
for n from 1 to 400 do
    if isA044821(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jan 18 2018

PARI

is(n) = { my(runs = List(), lr = 0, d = digits(n)); for(i = 1, #d - 1, if(d[i] != d[i + 1], listput(runs, i - lr); lr = i; ) ); listput(runs, #d - lr); #Set(runs) == #runs } \\ David A. Corneth, Jan 04 2021

Python

from itertools import groupby
def ok(n):
  runlengths = [len(list(g)) for k, g in groupby(str(n))]
  return len(runlengths) == len(set(runlengths))
print([i for i in range(1, 256) if ok(i)]) # Michael S. Branicky, Jan 04 2021