A334676 -id:A334676 - cp's OEIS frontend

A336580 Numbers k such that A334676(k) = 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 15, 24, 25, 35, 36, 45, 48, 72, 75, 125, 135, 140, 144, 175, 216, 225, 250, 270, 280, 288, 375, 384, 432, 540, 625, 675, 864, 875, 1080, 1125, 1250, 1296, 1350, 1575, 1620, 1680, 1728, 1750, 1800, 1875, 1944, 2160, 2250, 2500

Offset: 1

Rémy Sigrist, Jul 26 2020

All terms are 7-smooth (A002473).

This sequence is infinite as it contains the powers of 5.

			Regarding the number 540:
- 540 / 4 = 135,
- 135 / 3 = 45,
- 45 / 5 = 9,
- 9 / 9 = 1,
- so A334676(540) = 1
- and 540 belongs to this sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Illustration of terms < 1000
Rémy Sigrist, PARI program for A336580

Cf. A000351, A002473, A334676.

for (n=1, #keep=vector(2500, n, n==1), if (keep[n], print1 (n ", "); for (d=2, min(9, #keep\n), if (setsearch (Set(digits(nd=n*d)), d), keep[nd]=1))))

PARI
```
See Links section.
```

A387242 a(n) is the least k such that A334676(k) != k and the decimal string of n appears in A334676(k).

Original entry on oeis.org

2, 42, 26, 28, 102, 32, 85, 172, 95, 20, 22, 242, 26, 28, 302, 32, 85, 236, 95, 402, 42, 442, 115, 482, 502, 522, 162, 562, 145, 260, 62, 1615, 266, 268, 712, 272, 148, 772, 278, 802, 82, 842, 215, 882, 902, 92, 235, 962, 245, 1002, 102, 1042, 265, 1078, 1102, 112, 285, 1162

Offset: 1

Ali Sada, Aug 23 2025

			A334676(242) = 121, the first term whose decimal expansion contains the substring "12"; hence a(12) = 242.
A334676(21) = A334676(42) = 21 contains "2" but a(2) = 42 since the first does not satisfy A334676(k) != k.

Cf. A334676.

# uses A334676() and neighs() from A334676
from itertools import count, islice
def subs(s): yield from (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1))
def agen(): # generator of terms
    adict, n = dict(), 1
    for k in count(1):
        v = A334676(k)
        if v != k:
            for t in subs(str(v)):
                if (ti:=int(t)) not in adict:
                    adict[ti] = k
                    while n in adict:
                        yield adict[n]
                        n += 1
print(list(islice(agen(), 70))) # Michael S. Branicky, Aug 23 2025

A334684 a(n) is the least number that can be reached starting from n and iterating the nondeterministic map x -> x/d where d is a proper divisor of x whose decimal representation appears in that of x.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 6, 13, 14, 3, 16, 17, 18, 19, 10, 21, 11, 23, 6, 5, 13, 27, 14, 29, 10, 31, 16, 11, 34, 7, 6, 37, 38, 13, 10, 41, 21, 43, 11, 9, 46, 47, 6, 49, 10, 51, 13, 53, 54, 11, 56, 57, 58, 59, 10, 61, 31, 21, 16, 13, 11, 67, 68, 69

Offset: 1

Rémy Sigrist, Jul 25 2020

			For n = 140:
- 140 / 4 = 35, 35 / 5 = 7,
- 140 / 14 = 10,
- so a(140) = 7.

Rémy Sigrist, Table of n, a(n) for n = 1..10000

See A334676 for a similar sequence.

{ for (n=1, #a=vector(69, k, k), d=digits(n); s=setintersect(divisors(n), setbinop((u,v)->fromdigits(d[u..v]), [1..#d])); apply (t -> a[n]=min(a[n], a[n/t]), s[1..#s-1]); print1 (a[n]", ")) }

a(a(n)) = n.
a(10*k) <= 10 for any k > 0.
a(5^k) = 5 for any k > 0.
a(p) = p for any prime number p.

cp's OEIS Frontend

A336580 Numbers k such that A334676(k) = 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

PARI

A387242 a(n) is the least k such that A334676(k) != k and the decimal string of n appears in A334676(k).

Views

Author

Keywords

Examples

Crossrefs

Programs

Python

A334684 a(n) is the least number that can be reached starting from n and iterating the nondeterministic map x -> x/d where d is a proper divisor of x whose decimal representation appears in that of x.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula