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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 (list; graph; refs; listen; history; text; internal format)
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 * A031044 A194978 A195096

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

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Last modified September 24 15:40 EDT 2021. Contains 347643 sequences. (Running on oeis4.)