A054659 -id:A054659 - cp's OEIS frontend

A239664 a(n) = 1, a(n+1) = smallest number not occurring earlier, having with a(n) neither a common digit nor a common divisor.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 11, 20, 13, 22, 15, 26, 17, 24, 19, 25, 14, 27, 16, 29, 18, 35, 12, 37, 21, 34, 55, 28, 31, 40, 33, 41, 30, 47, 32, 45, 38, 49, 36, 59, 42, 53, 44, 39, 46, 51, 43, 50, 61, 48, 65, 71, 52, 63, 58, 67, 54, 73, 56, 79, 60, 77

Offset: 1

Reinhard Zumkeller, Mar 23 2014

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A054659, A067581, A276633, A276512.

import Data.List (delete, intersect); import Data.Function (on)
a239664 n = a239664_list !! (n-1)
a239664_list = 1 : f 1 [2..] where
   f v ws = g ws where
     g (x:xs) = if gcd v x == 1 && ((intersect `on` show) v x == "")
                   then x : f x (delete x ws) else g xs

{u=[]; a=1; for(n=1,99, print1(a","); u=setunion(u,[a]); while(#u>1&&u[2]==u[1]+1,u=u[^1]); for(k=u[1]+1,9e9, setsearch(u,k)&&next;gcd(k,a)>1&&next; #setintersect(Set(digits(a)),Set(digits(k)))&&next; a=k; next(2)));a} \\ M. F. Hasler, Sep 17 2016

A276512 a(n) = smallest integer not yet in the sequence with no digits in common with a(n-2); a(0)=0, a(1)=1.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 22, 20, 13, 14, 24, 23, 15, 16, 26, 25, 17, 18, 28, 27, 19, 30, 32, 12, 40, 33, 21, 29, 34, 31, 50, 42, 36, 35, 41, 44, 37, 38, 45, 46, 39, 51, 47, 43, 52, 55, 48, 49, 53, 56, 60, 70, 54, 58, 61, 62, 57, 59, 63, 64, 71, 72, 65, 66, 73, 74, 68, 69, 75

Offset: 0

Zak Seidov and Eric Angelini, Sep 06 2016

This is not a permutation of the nonnegative integers. E.g. 123456789 and 1023456789 (the smallest pandigital number) are not members.

a(n) = n for n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 34, 84, 104, 105, 1449, 2889, 3183, ...

Zak Seidov, Table of n, a(n) for n = 0..5000

Cf. A054659, A067581, A276633, A276766.

s={0,1};Do[a=s[[-2]];n=2; While[MemberQ[s,n]||Intersection [IntegerDigits[a],IntegerDigits[n]]≠{}, n++];AppendTo[s,n],{100}];s

from itertools import count, islice, product as P
def only(s, D=1): # numbers with >= D digits only from s
    yield from (int("".join(p)) for d in count(D) for p in P(s, repeat=d))
def agen(): # generator of terms
    aset, an1, an, minan = {0, 1}, 0, 1, 2
    yield from [0, 1]
    while True:
        an1, an, s = an, minan, set(str(an1))
        use = "".join(c for c in "0123456789" if c not in s)
        for an in only(use, D=len(str(minan))):
            if an not in aset: break
        aset.add(an)
        yield an
        while minan in aset: minan += 1
print(list(islice(agen(), 75))) # Michael S. Branicky, Jun 30 2022

A276766 a(n) = smallest nonnegative integer not yet in the sequence with no repeated digits and no digits in common with a(n-1), starting with a(0)=0.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 23, 14, 20, 13, 24, 15, 26, 17, 25, 16, 27, 18, 29, 30, 12, 34, 19, 28, 31, 40, 21, 35, 41, 32, 45, 36, 42, 37, 46, 38, 47, 39, 48, 50, 43, 51, 49, 52, 60, 53, 61, 54, 62, 57, 63, 58, 64, 59, 67, 80, 56, 70, 65, 71, 68, 72, 69, 73, 81, 74, 82, 75

Offset: 0

Claudio Meller, Sep 17 2016

The author of this sequence is Rodolfo Kurchan, who mentioned this sequence in a Facebook Group "Series", cf. link.

The sequence is finite, with last term a(5274) = 78642. - M. F. Hasler, Sep 17 2016

M. F. Hasler, Table of n, a(n) for n = 0..5274 (All terms)
Rodolfo Kurchan, Post in Facebook Group "Series".

Cf. A054659, A067581, A276633, A276512.

{u=[]; (t(k)=if(#Set(k=digits(k))==#k,k)); a=1; for(n=1, 99, print1(a","); u=setunion(u, [a]); t(u[1])||u[1]++; while(#u>1&&u[2]<=u[1]+1, u=u[^1]); for(k=u[1]+1, 9e9, setsearch(u, k)&&next; (d=t(k))&& !#setintersect(Set(digits(a)), Set(d))&&(a=k)&&next(2))); a} \\ M. F. Hasler, Sep 17 2016

def ok(s, t): return len(set(t)) == len(t) and len(set(s+t)) == len(s+t)
def agen(): # generator of complete sequence of terms
    aset, k, mink, MAX = {0}, 0, 1, 987654321
    while True:
        if k < MAX: yield k
        else: return
        k, s = mink, str(k)
        MAX = 10**(10-len(s))
        while k < MAX and (k in aset or not ok(s, str(k))):
            k += 1
        aset.add(k)
        while mink in aset: mink += 1
print(list(agen())[:73]) # Michael S. Branicky, Jun 30 2022

Edited by M. F. Hasler, Sep 17 2016

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A239664 a(n) = 1, a(n+1) = smallest number not occurring earlier, having with a(n) neither a common digit nor a common divisor.

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A276512 a(n) = smallest integer not yet in the sequence with no digits in common with a(n-2); a(0)=0, a(1)=1.

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A276766 a(n) = smallest nonnegative integer not yet in the sequence with no repeated digits and no digits in common with a(n-1), starting with a(0)=0.

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PARI

Python

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