A248323 Numbers n which appear at least twice in A037278(n), concatenation of their divisors written in base 10.

11, 12, 42, 84, 124, 135, 248, 325, 366, 510, 550, 555, 624, 650, 714, 1010, 1111, 1525, 1734, 2510, 3913, 4020, 5100, 5500, 5610, 5625, 8040, 11111, 13515, 16575, 21175, 24104, 25500, 28160, 34170, 35250, 35610, 36800, 37444, 44919, 50100, 51020, 51102, 51250, 52000

Offset

1,1

Comments

Overlapping is allowed, so a(1) = 11 is in the sequence, with concatenated divisors A037278(11) = "111".

All repunits (10^k-1)/9 = A000042(k) = A002275(k) with even k = number of digits (as to be divisible by 11) but not multiples of 3, i.e., k in A047235, have divisors {1, 11, ..., 1010...101, 1111...111} and therefore are in this sequence.

Numbers n = floor(10^(8+3k)/7), k>=0, also belong to this sequence; for k>=2m, the number n appears (at least) m+2 times in A037278(n). [Found by extending results from Hans Havermann.]

The smallest terms that appear more than twice in the concatenation are 1111, 400200, 800400, 28571428, all 3 times, and 42857142, 4 times. - Hans Havermann, Oct 05 2014

Links

Chai Wah Wu, Table of n, a(n) for n = 1..340

E. Angelini, Divisors showing a string, SeqFan list, Oct 03 2014

Example

The divisors of 42 are 1, 2, 3, 6, 7, 14, 21, 42, and "42" appears twice in their concatenation A037278(42) = "12367142142".

Prog

(PARI) is(n)={d=concat(apply(digits, divisors(n))); n=digits(n); for(j=0, #d-#n-1, for(i=1, #n, d[i+j]==n[i]||next(2)); return(1))}
(Python)
from sympy import divisors
import re
A248323_list = [n for n in range(1, 10**7) if len(list(re.finditer('(?='+str(n)+')', ''.join([str(d) for d in divisors(n)])))) > 1]
# Chai Wah Wu, Nov 01 2014

Crossrefs

Cf. A037278.

Sequence in context: A225299 A290336 A300405 * A291059 A041254 A041256

Adjacent sequences: A248320 A248321 A248322 * A248324 A248325 A248326

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Oct 04 2014

Status

approved