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

1,1

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.

Links

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

Example

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.

Prog

(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

Crossrefs

Cf. A047726, A179239, A241754, A241899.

Sequence in context: A253510 A253503 A195674 * A241754 A063365 A116869

Adjacent sequences: A319271 A319272 A319273 * A319275 A319276 A319277

Keyword

base,nonn,changed

Author

Pieter Post, Sep 16 2018

Extensions

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

Status

approved