|
|
A372106
|
|
A370972 terms composed of nine distinct digits which may repeat.
|
|
4
|
|
|
1476395008, 116508327936, 505627938816, 640532803911, 1207460451879, 1429150367744, 1458956660623, 3292564845031, 3820372951296, 5056734498816, 6784304541696, 8090702381056, 9095331446784, 10757095489536, 10973607685048, 13505488366293, 14913065975808, 38203732951296
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Each factorization is necessarily composed of multipliers that use only the single missing digit.
The single missing digit cannot be 0, 1, 5, or 6. Terms missing 2, 3, 4, 7, and 8 appear within a(1)-a(6). 52612606387341 = 9^6 * 99 * 999999 is an example of a term missing 9. - Michael S. Branicky, Apr 18 2024
Some terms are equal to the sum of two distinct smaller terms:
a(741) = a(635) + a(673)
a(1202) = a(1081) + a(1144)
a(1273) = a(1110) + a(1169)
a(1493) = a(1335) + a(1374)
a(2753) = a(2478) + a(2528)
a(2793) = a(2512) + a(2583)
a(3581) = a(3234) + a(3317)
a(4199) = a(3808) + a(3921)
a(4803) = a(4510) + a(4607) = a(4557) + a(4568)
a(5756) = a(5256) + a(5362)
a(6083) = a(5718) + a(5847)
a(7262) = a(6761) + a(6779)
a(7331) = a(6786) + a(6904)
a(9204) = a(8723) + a(8886)
a(9364) = a(8858) + a(8982)
|
|
LINKS
|
|
|
EXAMPLE
|
10973607685048 = 22222*22222*22222 is in the sequence because it has nine distinct digits and may be factored using only its missing digit.
|
|
PROG
|
(Python)
import heapq
from itertools import islice
def agen(): # generator of terms
allowed = [2, 3, 4, 7, 8, 9]
v, oldt, h, repunits, bigr = 1, 0, list((d, d) for d in allowed), [1], 1
while True:
v, d = heapq.heappop(h)
if (v, d) != oldt:
s = set(str(v))
if len(s) == 9 and str(d) not in s:
yield v
oldt = (v, d)
while v > bigr:
bigr = 10*bigr + 1
repunits.append(bigr)
for c in allowed:
heapq.heappush(h, (bigr*c, c))
for r in repunits:
heapq.heappush(h, (v*d*r, d))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|