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A061384 Numbers n such that sum of digits = number of digits. 16
1, 11, 20, 102, 111, 120, 201, 210, 300, 1003, 1012, 1021, 1030, 1102, 1111, 1120, 1201, 1210, 1300, 2002, 2011, 2020, 2101, 2110, 2200, 3001, 3010, 3100, 4000, 10004, 10013, 10022, 10031, 10040, 10103, 10112, 10121, 10130, 10202, 10211 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Number of d-digit entries is A071976(d). - Robert Israel, Apr 06 2016
Equivalently, numbers n > 0 for which the arithmetic mean of the digits equals 1. - M. F. Hasler, Dec 07 2018
LINKS
FORMULA
{n > 0 | A007953(n) = A055642(n)}. - M. F. Hasler, Dec 07 2018
EXAMPLE
120 is a term as the arithmetic mean of the digits is (1+2+0)/3 = 1.
MAPLE
Q:= proc(n, s) option remember;
# n-digit integers with digit sum s
if s = 0 then []
elif s = 1 then [10^(n-1)]
elif n = 1 then
if s <= 9 then [s]
else []
fi
else
map(op, [seq(map(t -> 10*t+i, procname(n-1, s-i)), i=0..min(9, s-1))])
fi
end proc:
map(op, [seq(sort(Q(n, n)), n=1..5)]); # Robert Israel, Apr 06 2016
MATHEMATICA
Select[Range[15000], Total[IntegerDigits[#]] == IntegerLength[#]&] (* Harvey P. Dale, Jan 08 2011 *)
PROG
(Magma) [ n: n in [1..10215] | &+Intseq(n) eq #Intseq(n) ]; // Bruno Berselli, Jun 30 2011
(PARI) isok(n) = (sumdigits(n)/#Str(n) == 1); \\ Michel Marcus, Mar 28 2016
(PARI) is_A061384(n)={sumdigits(n)==logint(n+!n, 10)+1} \\ M. F. Hasler, Dec 07 2018
(PARI) A061384_row(n)={my(L=List(), u=vector(n, i, i==1), d); forvec(v=vector(n+1, i, [if(i>n, n, 1), if(i>1, n, 1)]), vecmax(d=v[^1]-v[^-1]+u)<10 && listput(L, fromdigits(d)), 1); Vec(L)} \\ Return the list of all n-digit terms. - M. F. Hasler, Dec 07 2018
(Python)
from itertools import count, islice
def Q(n, s): # length-n strings of 0..9 with sum s, after Robert Israel
if s == 0: yield "0"*n
elif n == 1: yield (str(s) if s <= 9 else "")
else:
m = min(9, s) + 1
yield from (str(i)+t for i in range(m) for t in Q(n-1, s-i))
def agen():
yield from (int(t) for n in count(1) for t in Q(n, n) if t[0] != "0")
print(list(islice(agen(), 43))) # Michael S. Branicky, May 26 2022
(Python)
from itertools import count, islice
from collections import Counter
from sympy.utilities.iterables import partitions, multiset_permutations
def A061384_gen(): # generator of terms
for l in count(1):
for i in range(1, min(l, 9)+1):
yield from sorted(int(str(i)+''.join(map(str, j))) for s, p in partitions(l-i, k=9, size=True) for j in multiset_permutations([0]*(l-1-s)+list(Counter(p).elements())))
A061384_list = list(islice(A061384_gen(), 30)) # Chai Wah Wu, Nov 28 2023
CROSSREFS
Totally balanced subset: A071154. Cf. also A061383-A061388, A061423-A061425.
Cf. A071976.
Cf. A007953 (sum of digits), A055642 (number of digits).
Sequence in context: A180113 A198310 A085187 * A071154 A071161 A367609
KEYWORD
nonn,base,easy
AUTHOR
Amarnath Murthy, May 03 2001
EXTENSIONS
More terms from Erich Friedman, May 08 2001
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)