A249516 -id:A249516 - cp's OEIS frontend

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

Jaroslav Krizek, Oct 31 2014

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

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

Cf. A007953, A249516, A249517.

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

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

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

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

A249517 Numbers k for which the digital sum A007953(k) and the digital product A007954(k) both contain the same distinct digits as the number k.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11111111111

Offset: 1

Jaroslav Krizek, Oct 31 2014

a(12) = (10^106-1)/9 + 122222222. - Max Alekseyev, Nov 15 2014

Other entries include (10^111-1)/9, (10^113-1)/9 + 177, (10^115-1)/9 + 122222222, (10^117-1)/9 + 11117, (10^125-1)/9 + 2224, (10^126-1)/9 + 333335, (10^135-1)/9 + 4666, (10^143-1)/9 + 446, (10^143-1)/9 + 2224, (10^144-1)/9 + 33335. All other entries with 150 or fewer digits are formed by permutations of the decimal digits of these entries (including a(12)). (10^((10^m-1)/9)-1)/9 are entries of the sequence for m >= 0. - Chai Wah Wu, Nov 15 2014

			11111111111 is a term since A007953(11111111111) = 11 and A007954(11111111111) = 1.

Intersection of A249515 and A249516. Subsequence of A249334.

Cf. A007954, A249334, A249515, A249516.

[0] cat [n: n in [0..10^7] | Set(Intseq(n)) eq Set(Intseq(&*Intseq(n))) and Set(Intseq(n)) eq Set(Intseq(&+Intseq(n)))];

is(n)=if(n<=9,return(1)); my(d=digits(n),s=Set(d)); s==Set(digits(sum(i=1,#d,d[i]))) && s==Set(digits(prod(i=1,#d,d[i]))) \\ Charles R Greathouse IV, Nov 13 2014

from itertools import product
from operator import mul
from functools import reduce
A249517_list = [0]
for g in range(1,15):
    xp, ylist = [], []
    for i in range(9*g,-1,-1):
        x = set(str(i))
        if not (('0' in x) or (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 set(y) == x:
                        yd = [int(d) for d in y]
                        if set(str(sum(yd))) == x == set(str(reduce(mul, yd, 1))):
                            ylist.append(int(''.join(y)))
    A249517_list.extend(sorted(ylist)) # Chai Wah Wu, Nov 15 2014

a(11) = 11111111111 confirmed by Sean A. Irvine, Nov 13 2014, by direct search.

cp's OEIS Frontend

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

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