A319274 Osiris or Digit re-assembly numbers: numbers that are equal to the sum of permutations of subsamples of their own digits.

132, 264, 396, 8991, 10545, 35964, 255530, 1559844, 9299907, 47755078, 89599104, 167264994, 283797162, 473995260, 3929996070, 6379993620, 10009998999, 11111111110, 22222222220, 33333333330, 44444444440, 55555555550, 66666666660, 77777777770, 88888888880, 99999999990

Offset: 1

Author

Pieter Post, Sep 16 2018

Keywords

• base
• nonn

Comments

This sequence differs from A241754 because this sequence uses permutations only once.

Permutations are of the same length k, leading zeros are allowed.

The k's in the sequence are: 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 7, 10, 10, 10, 10, 10, 10, 10, 10, 10, 6, 7, 7, 8, 7, 9, 9.

Examples

			10545 = 014 + 015 + 041 + 045 + 051 + 054 + 055 + 104 + 105 + 140 + 145 + 150 + 154 + 155 + 401 + 405 + 410 + 415 + 450 + 451 + 455 + 501 + 504 + 505 + 510 + 514 + 515 + 540 + 541 + 545 + 550 + 551 + 554.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..33 (terms < 10^16)

Crossrefs

Cf. A047726, A179239, A241754, A241899.

Programs

Python

import itertools
def getData(a, b):
    dig = (itertools.permutations(str(a), b))
    for d in dig:
        yield d
for w in range(2, 6):
    kk=int(w*'1')
    for i in range (kk, 10**(w+3), kk):
        m=[]
        get = getData(i, w)
        while True:
            try:
                n = next(get)
                ee=int("".join((n)))
                if ee not in m:
                    m.append(ee)
            except StopIteration:
                if sum (m)==i and len(m)>1:
                    m.sort()
                    print (sum(m), len(m), m, i)
                break

Extensions

a(12)-a(26) from Giovanni Resta, Sep 16 2018