A372106 A370972 terms composed of nine distinct digits which may repeat.

1476395008, 116508327936, 505627938816, 640532803911, 1207460451879, 1429150367744, 1458956660623, 3292564845031, 3820372951296, 5056734498816, 6784304541696, 8090702381056, 9095331446784, 10757095489536, 10973607685048, 13505488366293, 14913065975808, 38203732951296

Offset: 1

Author

Hans Havermann, Apr 18 2024

Keywords

• nonn
• base

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)

a(9453) = a(8972) + a(8983) - Hans Havermann, Apr 21 2024

Examples

			10973607685048 = 22222*22222*22222 is in the sequence because it has nine distinct digits and may be factored using only its missing digit.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1016 from Hans Havermann)
• Michael S. Branicky and Hans Havermann, Table of n, a(n) for n = 1..10000, fully factored

Crossrefs

Cf. A370970, A370972.

Programs

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))
print(list(islice(agen(), 100))) # Michael S. Branicky, Apr 19 2024