A052220 Numbers whose sum of digits is 6.

6, 15, 24, 33, 42, 51, 60, 105, 114, 123, 132, 141, 150, 204, 213, 222, 231, 240, 303, 312, 321, 330, 402, 411, 420, 501, 510, 600, 1005, 1014, 1023, 1032, 1041, 1050, 1104, 1113, 1122, 1131, 1140, 1203, 1212, 1221, 1230, 1302, 1311, 1320, 1401, 1410

Offset: 1

Author

Henry Bottomley, Feb 01 2000

Keywords

• nonn
• base
• easy

Comments

A007953(a(n)) = 6; number of repdigits = #{6,33,222,111111} = A242627(6) = 4. - Reinhard Zumkeller, Jul 17 2014

There are binomial(t + 4, 5) terms having exactly t digits. Therefore binomial(t + 5, 6) have at most t digits. - David A. Corneth, Jun 29 2025

Examples

			1023 is in the sequence as it has digital sum 1 + 0 + 2 + 3 = 6. - _David A. Corneth_, Jun 29 2025
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..12376 (terms 1..924 from Vincenzo Librandi; all terms with <= 12 digits)

Crossrefs

Cf. A007953.

Cf. A011557 (1), A052216 (2), A052217 (3), A052218 (4), A052219 (5), 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

a052220 n = a052220_list !! (n-1)
a052220_list = filter ((== 6) . a007953) [0..]
-- Reinhard Zumkeller, Jul 17 2014

Magma

[n: n in [1..1500] | &+Intseq(n) eq 6 ]; // Vincenzo Librandi, Mar 07 2013

Mathematica

Select[Range[10^4], Total[IntegerDigits[#]] == 6 &] (* Vincenzo Librandi, Mar 07 2013 *)

PARI

nxt(n) = {my(v, c, toadd); v = valuation(n, 10); c = (n / 10^v)%10; toadd = 10^(v)*(10 - c) + c - 1; return(n + toadd)} \\ David A. Corneth, Jun 29 2025

Python

from sympy.utilities.iterables import multiset_permutations
def auptodigs(maxdigits):
    alst = []
    for d in range(1, maxdigits+1):
        digset = "0"*(d-1) + "11111122233456"
        for p in multiset_permutations(digset, d):
            if p[0] != '0' and sum(map(int, p)) == 6:
                alst.append(int("".join(p)))
    return alst
print(auptodigs(4)) # Michael S. Branicky, Jun 15 2021

Formula

a(n) = a(n-1) + 10^v * (10 - c) + c-1 where c is the last nonzero digit of a(n) and v is the 10-adic valuation of a(n-1) and n > 1. - David A. Corneth, Jun 29 2025

Extensions

Offset changed by Bruno Berselli, Mar 07 2013