login
A249517
Numbers n for which the digital sum A007953(n) and the digital product A007954(n) both contain the same distinct digits as the number n.
2
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11111111111
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^n-1)/9)-1)/9 are entries of the sequences for n > 1. - Chai Wah Wu, Nov 15 2014
EXAMPLE
11111111111 is a term since A007953(11111111111) = 11 and A007954(11111111111) = 1.
PROG
(Magma) [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
Intersection of A249515 and A249516. Subsequence of A249334.
Sequence in context: A276142 A227549 A110370 * A353907 A363271 A031044
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