A052219 Numbers whose sum of digits is 5.

5, 14, 23, 32, 41, 50, 104, 113, 122, 131, 140, 203, 212, 221, 230, 302, 311, 320, 401, 410, 500, 1004, 1013, 1022, 1031, 1040, 1103, 1112, 1121, 1130, 1202, 1211, 1220, 1301, 1310, 1400, 2003, 2012, 2021, 2030, 2102, 2111, 2120, 2201, 2210, 2300, 3002

Offset: 1

Author

Henry Bottomley, Feb 01 2000

Keywords

• nonn
• base
• easy

Comments

A007953(a(n)) = 5; number of repdigits = #{5,11111} = A242627(5) = 2. - Reinhard Zumkeller, Jul 17 2014

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..11628 (all terms through 15 digits; terms 1..1287 from Vincenzo Librandi and T. D. Noe, terms 1..462 from Vincenzo Librandi)

Crossrefs

Cf. A007953.

Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052220 (6), A052221 (7), A052222 (8), A052223 (9), A052224 (10), A166311 (11), A235151 (12), A143164 (13), A235225(14), A235226 (15), A235227 (16), A166370 (17), A235228 (18), A166459 (19), A235229 (20).

Cf. A242614, A242627.

Programs

Haskell

a052219 n = a052219_list !! (n-1)
a052219_list = filter ((== 5) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

Magma

[n: n in [1..3010] | &+Intseq(n) eq 5 ]; // Vincenzo Librandi, Mar 07 2013

Mathematica

Select[Range[10^4], Total[IntegerDigits[#]] == 5 &] (* Vincenzo Librandi, Mar 07 2013 *)
Union[Flatten[Table[FromDigits /@ Permutations[PadRight[s, 9]], {s, IntegerPartitions[5]}]]] (* T. D. Noe, Mar 08 2013 *)

PARI

isok(n) = sumdigits(n) == 5; \\ Michel Marcus, Dec 28 2015

Python

from sympy.utilities.iterables import multiset_permutations
def auptodigs(maxdigits):
  alst = [5]
  for d in range(2, maxdigits+1):
    fulldigset = list("0"*(d-1) + "1111122345")
    for firstdig in "12345":
      target_sum, restdigset = 5-int(firstdig), fulldigset[:]
      restdigset.remove(firstdig)
      for p in multiset_permutations(restdigset, d-1):
        if sum(map(int, p)) == target_sum:
          alst.append(int(firstdig+"".join(p)))
          if int(p[0]) == target_sum: break
  return alst
print(auptodigs(4)) # Michael S. Branicky, May 14 2021

Extensions

Offset changed from Bruno Berselli, Mar 07 2013