A276633 -id:A276633 - cp's OEIS frontend

A276769 Next larger number having the same digits as n.

11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 111, 21, 31, 41, 51, 61, 71, 81, 91, 200, 112, 222, 32, 42, 52, 62, 72, 82, 92, 300, 113, 223, 333, 43, 53, 63, 73, 83, 93, 400, 114, 224, 334, 444, 54, 64, 74, 84, 94, 500, 115, 225, 335, 445, 555, 65, 75, 85, 95, 600, 116, 226, 336, 446, 556, 666, 76, 86, 96, 700

Offset: 1

David A. Corneth, Sep 20 2016

This sequence can be used to find terms of A276633. Each number in base 10 can have 1024 sets of digits, either {0}, {1}, ..., or {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Some occur once or never in A276633. For each such set the least number having its digits can be chosen. Then from that set put the next higher number having the digits only of that set.

			No number between (exclusive) 31 and 113 has the digits of 31; {1, 3}. 113 has. Therefore, a(31) = 113.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A276633.

N:= 1000: # to get a(1)..a(m-1) where a(m) is the first term > N
for s in combinat:-powerset({$0..9}) do R[s]:= NULL od:
for n from 1 to N do
s:= convert(convert(n,base,10),set);
R[s]:= R[s], n;
if R[s] <> n then A[R[s][-2]]:= n fi
od:
seq(A[i],i=1..min(remove(t-> A[t]::integer, [$1..N]))-1); # Robert Israel, Nov 08 2016

a(n) = {my(m=vecsort(digits(n), ,8), i = n+1); while(vecsort(digits(i), ,8)!=m,i++); i}

A298482 a(n) = smallest integer not yet in the sequence with no digits in common with a(n-1), a(n-2), and a(n-3); a(0)=0, a(1)=1, a(2)=2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 33, 44, 11, 20, 35, 46, 17, 28, 30, 45, 16, 27, 38, 40, 15, 26, 37, 48, 19, 25, 36, 47, 18, 29, 50, 34, 61, 72, 55, 39, 14, 60, 52, 73, 41, 66, 58, 23, 49, 67, 51, 32, 80, 64, 57, 12, 83, 69, 54, 21, 70, 63, 59, 24, 71, 68

Offset: 0

Enrique Navarrete, Feb 28 2018

The first differences of this sequence are symmetrically distributed around 0, in a distribution that has a larger kurtosis than the Normal distribution.

Cf. A067581, A276633.

A342755 a(1) = 2; for n > 1, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-1) and a(n-1)*a(n) shares no digit with either a(n-1) or a(n).

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 8, 9, 42, 15, 22, 14, 55, 12, 37, 16, 25, 36, 29, 47, 23, 46, 13, 44, 18, 32, 17, 38, 19, 33, 26, 35, 174, 53, 76, 59, 34, 27, 43, 67, 49, 62, 87, 106, 493, 57, 24, 75, 48, 65, 122, 39, 54, 72, 88, 45, 66, 73, 56, 77, 52, 79, 84, 63, 78, 123, 69, 58, 64, 92, 74, 68, 114, 85, 314

Offset: 1

Scott R. Shannon, Mar 20 2021

No term can end in 0 or 1 as that would result in the last digit of a(n-1)*a(n) being the same as a(n)'s last digit. Currently the last known term is a(173) = 922989, the next being at least 5*10^10 if it exists. It is unknown if the sequence is infinite.

a(174) = 60060666070067077 and a(175) has 52 digits (see b-file). If a(176) exists, it is > 10^71. - Michael S. Branicky, Apr 10 2023

			a(2) = 3 as 3 shares no digit with a(1) = 2 and a(1)*3 = 2*3 = 6 shares no digit with a(1) = 2 or 3.
a(9) = 42 as 42 shares no digit with a(8) = 9 and a(8)*42 = 9*42 = 378 shares no digit with a(8) = 9 or 42.
a(10) = 15 as 15 shares no digit with a(9) = 42 and a(9)*15 = 42*15 = 630 shares no digit with a(9) = 42 or 15. This is the first term that differs from A342442.
a(173) = 922989 as 922989 shares no digit with a(172) = 7154 and a(172)*922989 = 7154*922989 = 6603063306 shares no digit with a(172) = 7154 or 922989. This is currently the last known term.

Michael S. Branicky, Table of n, a(n) for n = 1..175

Cf. A342442, A342441, A276633, A010784, A043537, A043096, A338466, A336285.

def aupton(terms):
  alst, aset = [2], {2}
  while len(alst) < terms:
    an, anm1_digs = 2, set(str(alst[-1]))
    while True:
      while an in aset: an += 1
      an_digs = set(str(an))
      if (an_digs & anm1_digs) == set():
        prod_digs = set(str(an*alst[-1]))
        if (anm1_digs | an_digs) & prod_digs  == set():
          alst.append(an); aset.add(an); break
      an += 1
  return alst
print(aupton(173)) # Michael S. Branicky, Mar 21 2021

A301801 a(n) = smallest integer not yet in the sequence with no digits in common with a(n-1), a(n-2), a(n-3), and a(n-4); a(0)=0, a(1)=1, a(2)=2, a(3)=3.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 22, 33, 44, 55, 11, 20, 36, 47, 58, 19, 200, 63, 74, 85, 91, 202, 66, 34, 57, 18, 29, 60, 43, 75, 81, 92, 600, 333, 45, 17, 28, 69, 30, 54, 71, 82, 96, 300, 444, 15, 27, 68, 39, 40, 51, 72, 86, 93, 400, 111, 25, 67, 38, 49, 100

Offset: 0

Enrique Navarrete, Mar 26 2018

The first differences of this sequence are symmetrically distributed in a distribution that has a larger kurtosis than the Normal distribution.
It seems that appart from the initial terms, 39 and 40 are the only consecutive terms.
Unlike A298482, 3-digit terms appear as early as a(22)=200.

Rémy Sigrist, PARI program for A301801

Cf. A067581, A276633, A298482.

Nest[Append[#, Block[{k = 4, d}, While[Nand[FreeQ[#, k], ! IntersectingQ[Union@ Apply[Join, Take[#[[All, -1]], -4] ], Set[d, IntegerDigits[k]]] ], k++]; {k, d}]] &, Transpose@ {#, IntegerDigits@ #} &@ Range[0, 3], 62][[All, 1]] (* Michael De Vlieger, Apr 12 2018 *)

PARI
```
See Links section.
```

cp's OEIS Frontend

A276769 Next larger number having the same digits as n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

PARI

A298482 a(n) = smallest integer not yet in the sequence with no digits in common with a(n-1), a(n-2), and a(n-3); a(0)=0, a(1)=1, a(2)=2.

Views

Author

Keywords

Comments

Crossrefs

A342755 a(1) = 2; for n > 1, a(n) is the least positive integer not occurring earlier such that a(n) shares no digit with a(n-1) and a(n-1)*a(n) shares no digit with either a(n-1) or a(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

A301801 a(n) = smallest integer not yet in the sequence with no digits in common with a(n-1), a(n-2), a(n-3), and a(n-4); a(0)=0, a(1)=1, a(2)=2, a(3)=3.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI