A249515 Numbers k for which the digital sum of k contains the same distinct digits as k itself.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 199, 919, 991, 1188, 1818, 1881, 2999, 8118, 8181, 8811, 9299, 9929, 9992, 11177, 11444, 11717, 11771, 13333, 14144, 14414, 14441, 17117, 17171, 17711, 22888, 26666, 28288, 28828, 28882, 31333, 33133, 33313, 33331, 39999, 41144

Offset: 1

Author

Jaroslav Krizek, Oct 31 2014

Keywords

• nonn
• base
• easy

Examples

			199 is in the sequence since 1 + 9 + 9 = 19.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..4477

Crossrefs

Cf. A007953, A249516, A249517.

Programs

Magma

[k: k in [0..1000000] | Set(Intseq(k)) eq Set(Intseq(&+Intseq(k)))];

Mathematica

Select[Range[1000], Union[IntegerDigits[#]] == Union[Plus@@IntegerDigits[#]] &] (* Alonso del Arte, Nov 02 2014 *)

PARI

for(n=0, 5*10^4, if(vecsort(digits(n),,8) ==vecsort(digits(sumdigits(n)),,8), print1(n,", "))) \\ Derek Orr, Nov 02 2014

Python

from itertools import product
A249515_list = [0]
for g in range(1,12):
    xp, ylist = [], []
    for i in range(9*g,-1,-1):
        x = set(str(i))
        if not x in xp:
            xv = [int(d) for d in x]
            imin = int(''.join(sorted(str(i))))
            if max(xv)*(g-len(x)) >= imin-sum(xv) and i-sum(xv) >=  min(xv)*(g-len(x)):
                xp.append(x)
                for y in product(x,repeat=g):
                    if y[0] != '0' and set(y) == x and set(str(sum([int(d) for d in y]))) == x:
                        ylist.append(int(''.join(y)))
    A249515_list.extend(sorted(ylist)) # Chai Wah Wu, Nov 15 2014