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

1,2

Links

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

Example

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

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

Prog

(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
(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

Crossrefs

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

Sequence in context: A353181 A306273 A141033 * A297148 A048307 A043713

Adjacent sequences: A044818 A044819 A044820 * A044822 A044823 A044824

Keyword

nonn,base

Author

Clark Kimberling

Status

approved