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.

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

Links

Table of n, a(n) for n=1..11.

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.

Cf. A007954, A249334, A249515, A249516.

Sequence in context: A276142 A227549 A110370 * A353907 A363271 A031044

Adjacent sequences: A249514 A249515 A249516 * A249518 A249519 A249520

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