A007091 -id:A007091 - cp's OEIS frontend

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

Clark Kimberling

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

Cf. A007091.

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

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 *)

A043356 Numbers having four 1's in base 5.

Original entry on oeis.org

156, 656, 756, 776, 780, 782, 783, 784, 786, 791, 796, 806, 831, 856, 906, 1031, 1156, 1406, 2031, 2656, 3156, 3256, 3276, 3280, 3282, 3283, 3284, 3286, 3291, 3296, 3306, 3331, 3356, 3406, 3531, 3656, 3756, 3776, 3780

Offset: 1

Clark Kimberling

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

Cf. A007091 (numbers in base 5).

F:= proc(d,m) option remember;
  local A,B;
  if m > d then return [] fi;
  if d = 0 then return [0] fi;
  A:= seq(seq(seq(t+i*5^(d-1),t=procname(dd,m)),dd = 0..d-1),i=2..4);
  if m = 0 then [A]
  else [seq(seq(t+5^(d-1),t=procname(dd,m-1)),dd=0..d-1),A]
  fi
end proc:
map(op,[seq(F(d,4),d=4..6)]); # Robert Israel, Jul 02 2018

Select[Range[4000],DigitCount[#,5,1]==4&] (* Harvey P. Dale, Apr 28 2025 *)

isok(n) = #select(x->(x==1), digits(n, 5)) == 4; \\ Michel Marcus, Jul 02 2018

A043364 Numbers having four 3's in base 5.

Original entry on oeis.org

468, 1093, 1718, 1968, 2093, 2218, 2268, 2293, 2318, 2328, 2333, 2338, 2340, 2341, 2342, 2344, 2348, 2368, 2468, 2968, 3593, 4218, 4843, 5093, 5218, 5343, 5393, 5418, 5443, 5453, 5458, 5463, 5465, 5466, 5467, 5469, 5473

Offset: 1

Clark Kimberling

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

Cf. A007091.

isok(k) = #select(x->(x==3), digits(k, 5)) == 4; \\ Michel Marcus, Apr 24 2021

A043532 Number of distinct base-5 digits of n.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 3, 3, 2, 1, 2, 2, 2, 3, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 3, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 3, 2, 2, 3, 2

Offset: 1

Clark Kimberling

Cf. A007091.

f[n_]:=Length[Select[DigitCount[n,5],#!=0&]]; Array[f,100] (* Harvey P. Dale, May 11 2011 *)

A043605 Numbers whose base-5 representation has exactly 5 runs.

Original entry on oeis.org

651, 652, 653, 654, 660, 661, 663, 664, 665, 666, 667, 669, 670, 671, 672, 673, 676, 677, 678, 679, 680, 682, 683, 684, 690, 691, 692, 694, 695, 696, 697, 698, 701, 702, 703, 704, 705, 707, 708, 709, 710, 711, 713, 714, 720

Offset: 1

Clark Kimberling

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

Cf. A007091.

fBC:= proc(b,c) local t,i,j,m;
    m:= 1/5; t:= 0:
    for i from 1 to 5 do
       for j from 1 to c[i] do
         m:= 5*m;
         t:= t + b[i]*m;
    od od;
  t
end proc:
F:= proc(n) local Res, a,b,c, q, B,C;
  Res:= NULL;
  B:= [seq(seq(seq(seq(seq([a[1],a[2],a[3],a[4],a[5]],a[1]=subs(a[2]=NULL,[$0..4])),a[2]=subs(a[3]=NULL,[$0..4])),a[3]=subs(a[4]=NULL,[$0..4])),a[4]=subs(a[5]=NULL,[$0..4])),a[5]=1..4)];
  sort([seq(seq(fBC(b,c),b=B),c=combinat:-composition(n,5))])
end proc:
op(F(5)),op(F(6)); # Robert Israel, Jan 22 2019

Select[Range[1000],Length[Split[IntegerDigits[#,5]]]==5&] (* Harvey P. Dale, Jan 02 2014 *)

A045161 Numbers whose base-5 representation contains exactly one 0 and no 1's.

Original entry on oeis.org

0, 10, 15, 20, 52, 53, 54, 60, 65, 70, 77, 78, 79, 85, 90, 95, 102, 103, 104, 110, 115, 120, 262, 263, 264, 267, 268, 269, 272, 273, 274, 302, 303, 304, 310, 315, 320, 327, 328, 329, 335, 340, 345, 352, 353, 354, 360, 365, 370, 387

Offset: 1

Clark Kimberling

Vincenzo Librandi, Table of n, a(n) for n = 1..7798

Cf. A007091.

Select[Range[0, 400], DigitCount[#, 5, 0]==1 && DigitCount[#, 5, 1]==0 &] (* Vincenzo Librandi, Jun 29 2019 *)

a(1) = 0 inserted by Georg Fischer, Jun 28 2019

A045177 Numbers whose base-5 representation contains exactly one 0 and one 2.

Original entry on oeis.org

10, 27, 35, 51, 53, 54, 55, 65, 70, 77, 85, 102, 110, 132, 136, 138, 139, 142, 147, 152, 160, 176, 178, 179, 180, 190, 195, 202, 210, 227, 235, 256, 258, 259, 266, 268, 269, 271, 273, 274, 276, 278, 279, 280, 290, 295, 326, 328, 329, 330, 340, 345, 351, 353

Offset: 1

Clark Kimberling

Cf. A007091.

Subsequence of A039284.

from sympy.ntheory import count_digits
def ok(n): c = count_digits(n, b=5); return c[0] == c[2] == 1
print([k for k in range(354) if ok(k)]) # Michael S. Branicky, Oct 27 2021

A045187 Numbers whose base-5 representation contains exactly three 0's and three 2's.

Original entry on oeis.org

6262, 6302, 6310, 6502, 6510, 6550, 7502, 7510, 7550, 7750, 15687, 15887, 15927, 15935, 16887, 16927, 16935, 17127, 17135, 17175, 21887, 21927, 21935, 22127, 22135, 22175, 23127, 23135, 23175, 23375, 31287, 31307

Offset: 1

Clark Kimberling

			6262_10 = 200022_5.

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Cf. A007091.

Select[Range[35000],DigitCount[#,5,0]==DigitCount[#,5,2]==3&] (* Harvey P. Dale, Jul 23 2014 *)

A045203 Numbers whose base-5 representation contains no 0's and exactly one 4.

Original entry on oeis.org

4, 9, 14, 19, 21, 22, 23, 34, 39, 44, 46, 47, 48, 59, 64, 69, 71, 72, 73, 84, 89, 94, 96, 97, 98, 106, 107, 108, 111, 112, 113, 116, 117, 118, 159, 164, 169, 171, 172, 173, 184, 189, 194, 196, 197, 198, 209, 214, 219, 221, 222, 223

Offset: 1

Clark Kimberling

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A007091.

Select[Range[300],DigitCount[#,5,0]==0&&DigitCount[#,5,4]==1&] (* Harvey P. Dale, Jun 24 2014 *)

A045207 Numbers whose base-5 representation contains exactly one 0 and one 4.

Original entry on oeis.org

20, 29, 45, 54, 70, 79, 95, 101, 102, 103, 105, 110, 115, 134, 139, 144, 146, 147, 148, 154, 170, 179, 195, 204, 220, 226, 227, 228, 230, 235, 240, 259, 264, 269, 271, 272, 273, 279, 295, 304, 320, 329, 345, 351, 352, 353, 355

Offset: 1

Clark Kimberling

Subset of A039286. - R. J. Mathar, Oct 20 2008

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

Cf. A007091.

F:= proc(d) local S, i,j;
   # to get all d-digit members
   S:= select(t -> t[d]<>0, map(op@combinat:-permute,[seq(seq([0,4,1$i,2$j,3$(d-2-i-j)],j=0..d-2-i),i=0..d-2)]));
   sort(map(t -> add(t[i]*5^(i-1),i=1..d), S))
end proc:
seq(op(F(d)),d=2..5); # Robert Israel, Aug 02 2020

Select[Range[400],DigitCount[#,5,0]==DigitCount[#,5,4]==1&] (* Harvey P. Dale, Nov 10 2017 *)

cp's OEIS Frontend

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

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Mathematica

A043356 Numbers having four 1's in base 5.

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Maple

Mathematica

PARI

A043364 Numbers having four 3's in base 5.

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PARI

A043532 Number of distinct base-5 digits of n.

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Mathematica

A043605 Numbers whose base-5 representation has exactly 5 runs.

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Maple

Mathematica

A045161 Numbers whose base-5 representation contains exactly one 0 and no 1's.

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Mathematica

Extensions

A045177 Numbers whose base-5 representation contains exactly one 0 and one 2.

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Python

A045187 Numbers whose base-5 representation contains exactly three 0's and three 2's.

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Mathematica

A045203 Numbers whose base-5 representation contains no 0's and exactly one 4.

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Mathematica

A045207 Numbers whose base-5 representation contains exactly one 0 and one 4.

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