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
Examples
199 is in the sequence since 1 + 9 + 9 = 19.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..4477
Programs
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Magma
[k: k in [0..1000000] | Set(Intseq(k)) eq Set(Intseq(&+Intseq(k)))];
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Mathematica
Select[Range[1000], Union[IntegerDigits[#]] == Union[Plus@@IntegerDigits[#]] &] (* Alonso del Arte, Nov 02 2014 *)
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PARI
for(n=0, 5*10^4, if(vecsort(digits(n),,8) ==vecsort(digits(sumdigits(n)),,8), print1(n,", "))) \\ Derek Orr, Nov 02 2014
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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