|
| |
|
|
A061384
|
|
Numbers n such that sum of digits = number of digits.
|
|
13
|
|
|
|
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
|
Robert Israel, Table of n, a(n) for n = 1..10000
|
|
|
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
|
|
|
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 A125886
Adjacent sequences: A061381 A061382 A061383 * A061385 A061386 A061387
|
|
|
KEYWORD
|
nonn,base,easy
|
|
|
AUTHOR
|
Amarnath Murthy, May 03 2001
|
|
|
EXTENSIONS
|
More terms from Erich Friedman, May 08 2001
|
|
|
STATUS
|
approved
|
| |
|
|
