A043107 Numbers k such that 0 and 2 occur juxtaposed in the base-5 representation of k but not of k-1.

10, 27, 35, 50, 60, 77, 85, 102, 110, 127, 135, 152, 160, 175, 185, 202, 210, 227, 235, 250, 277, 285, 300, 310, 327, 335, 352, 360, 377, 385, 402, 410, 425, 435, 452, 460, 477, 485, 502, 510, 527, 535, 550, 560, 577, 585, 602

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007091.

Programs

Maple

has02:= proc(n) local L,i,state;
  L:= convert(n,base,5);
  state:= 1;
  for i from 1 to nops(L) do
    if L[i] = 0 then
      if state = 2 then return true
      else state:= 0
      fi
    elif L[i] = 2 then
      if state = 0 then return true
      else state:= 2
      fi
    else state:= 1;
    fi
  od;
  false
end proc:
H:= select(has02, {$1..1001}):
sort(convert(H minus map(`+`,H,1),list)); # Robert Israel, Jan 20 2019

Mathematica

With[{s = Partition[Array[IntegerDigits[#, 5] &, 602], 2, 1]}, Map[FromDigits[#, 5] &, Select[s, And[And[SequenceCount[#1, {0, 2}] == 0, SequenceCount[#1, {2, 0}] == 0], Or[SequenceCount[#2, {0, 2}] > 0, SequenceCount[#2, {2, 0}] > 0]] & @@ # &][[All, -1]] ] ] (* Michael De Vlieger, Jan 20 2019 *)