OFFSET
1,3
COMMENTS
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
PROG
(Magma) [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)))];
(PARI) 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
(Python)
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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Jaroslav Krizek, Oct 31 2014
EXTENSIONS
a(11) = 11111111111 confirmed by Sean A. Irvine, Nov 13 2014, by direct search.
STATUS
approved
