This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
import Data.List (elemIndex); import Data.Maybe (fromJust) a227118 = (+ 1) . fromJust . (`elemIndex` a184992_list)
a(14) = 13, since a(13) = 20 and all integers smaller than 13 have a digit in common with 20 or have already appeared in the sequence.
import Data.List (delete, intersect); import Data.Function (on)
a067581 n = a067581_list !! (n-1)
a067581_list = 1 : f 1 [2..] where
f u vs = v : f v (delete v vs)
where v : _ = filter (null . (intersect `on` show) u) vs
-- Reinhard Zumkeller, Jul 01 2013
f[s_List] := Block[{k = 1, id = IntegerDigits@ s[[ -1]]}, While[ MemberQ[s, k] || Intersection[id, IntegerDigits@k] != {}, k++ ]; Append[s, k]]; Nest[f, {1}, 71] (* Robert G. Wilson v, Apr 03 2009 *)
{u=0; a=0; for(n=0, 99, print1(a", "); u+=1<M. F. Hasler, Nov 01 2014
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, an, minan = {0}, 0, 1
while True:
yield an
an, s = minan, set(str(an))
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)
while minan in aset: minan += 1
print(list(islice(agen(), 73))) # Michael S. Branicky, Jun 30 2022
import Data.List (intersect, delete)
a249591 n = a249591_list !! (n-1)
a249591_list = 1 : f 1 [2..] where
f x zs = g zs where
g (y:ys) = if null $ show y `intersect` show (x - 1)
then g ys else y : f y (delete y zs)
-- Reinhard Zumkeller, Nov 02 2014
{u=0; a=1; for(n=1, 99, print1(a","); u+=1<1,digits(a-1))); for(k=2, 9e9, bittest(u, k)&&next; #setintersect(D, Set(digits(k)))||next; a=k; break))}
18 is in the sequence because the common prime distinct divisors between a(2)=12 and a(3)=18 are 2 and 3.
with(numtheory):a0:={2,3}:lst:={}:
for n from 6 to 100 do:
ii:=0:
for k from 3 to 50000 while(ii=0) do:
y:=factorset(k):n0:=nops(y):lst1:={}:
for j from 1 to n0 do:
lst1:=lst1 union {y[j]}:
od:
a1:=a0 intersect lst1:
if {k} intersect lst ={} and a1 <> {} and nops(a1)=2
then
printf(`%d, `,k):lst:=lst union {k}:a0:=lst1:ii:=1:
else
fi:
od:
od:
f[s_List]:=Block[{m=s[[-1]],k=6},While[MemberQ[s,k]||Intersection[Transpose[FactorInteger[k]][[1]],Transpose[FactorInteger[m]][[1]]]=={}|| Length[Intersection[Transpose[FactorInteger[k]][[1]],Transpose[FactorInteger[m]][[1]]]]!=2,k++];Append[s,k]];Nest[f,{6},71]
lista(nn) = {a = 6; print1(a, ", "); fa = (factor(a)[,1])~; va = [a]; k = 0; while (k != nn, k = 1; while (!((#setintersect(fa, (factor(k)[,1])~) == 2) && (! vecsearch(va, k))), k++); a = k; print1(a, ", "); fa = (factor(a)[,1])~; va = vecsort(concat(va, k)););} \\ Michel Marcus, Nov 23 2015
Gathering intervals of consecutive integers, sequence begins as follows: 1, 10..12, 2, 20..23, 3, 13, 30..34, 4, 14, 24, 40..45, 5, 15, 25, 35, 50..56, 6, 16, 26, 36, 46, 60..67, 7, 17, 27, 37, 47, 57, 70..78, 8, 18, 28, 38, 48, 58, 68, 80..89, 9, 19, 29, 39, 49, 59, 69, 79, 90..99, 109, 119, 129, ...
a = {1}; Do[k = 2; While[Nand[! MemberQ[a, k], MemberQ[IntegerDigits[k], Max@ IntegerDigits[a[[n - 1]] ]]], k++]; AppendTo[a, k], {n, 2, 102}]; a (* Michael De Vlieger, Jul 22 2017 *)
. n | a(2n) a(2n+1) | GCD | not occurring after step n
. ---+---------------+-----+-------------------------------------------
. 0 | _ 1 | _ | {2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,..}
. 1 | 2 4 | 2 | {3,5,6,7,8,9,10,11,12,13,14,15,16,17,..}
. 2 | 3 6 | 3 | {5,7,8,9,10,11,12,13,14,15,16,17,18,19,..}
. 3 | 5 10 | 5 | {7,8,9,11,12,13,14,15,16,17,18,19,20,..}
. 4 | 7 14 | 7 | {8,9,11,12,13,15,16,17,18,19,20,21,22,..}
. 5 | 8 12 | 4 | {9,11,13,15,16,17,18,19,20,21,22,23,24..}
. 6 | 9 15 | 3 | {11,13,16,17,18,19,20,21,22,23,24,25,..}
. 7 | 11 22 | 11 | {13,16,17,18,19,20,21,23,24,25,26,27,..}
. 8 | 13 26 | 11 | {16,17,18,19,20,21,23,24,25,27,28,29,..}
. 9 | 16 18 | 2 | {17,19,20,21,23,24,25,27,28,29,30,31,..} .
import Data.List (delete)
a227113 n = a227113_list !! (n-1)
a227113_list = 1 : f [2..] where
f (x:xs) = x : y : f (delete y xs)
where y : _ = filter ((> 1) . (gcd x)) xs
Block[{a = {1, 10}, m = {1, 0}, k}, Do[k = 2; While[Nand[FreeQ[a, k], GCD[k, a[[-1]]] > 1, IntersectingQ[m, IntegerDigits[k]]], k++]; AppendTo[a, k]; Set[m, IntegerDigits[k]], {i, 73}]; a] (* Michael De Vlieger, Mar 11 2021 *)
from sympy import factorint
def aupton(terms):
alst, aset = [1, 10], {1, 10}
for n in range(3, terms+1):
an = 1
anm1_digs, anm1_factors = set(str(alst[-1])), set(factorint(alst[-1]))
while True:
while an in aset: an += 1
if set(str(an)) & anm1_digs != set():
if set(factorint(an)) & anm1_factors != set():
alst.append(an); aset.add(an); break
an += 1
return alst
print(aupton(75)) # Michael S. Branicky, Mar 09 2021
Block[{a = {1, 2}, m = {2}, k}, Do[k = 2; While[Nand[FreeQ[a, k], GCD[k, a[[-1]]] > 1, ! IntersectingQ[m, IntegerDigits[k]]], k++]; AppendTo[a, k]; Set[m, IntegerDigits[k]], {i, 74}]; a] (* Michael De Vlieger, Mar 11 2021 *)
from sympy import factorint
def aupton(terms):
alst, aset = [1, 2], {1, 2}
for n in range(3, terms+1):
an = 1
anm1_digs, anm1_factors = set(str(alst[-1])), set(factorint(alst[-1]))
while True:
while an in aset: an += 1
if set(str(an)) & anm1_digs == set():
if set(factorint(an)) & anm1_factors != set():
alst.append(an); aset.add(an); break
an += 1
return alst
print(aupton(76)) # Michael S. Branicky, Mar 09 2021
Block[{a = {1}, m = {1}, k}, Do[k = 2; While[Nand[FreeQ[a, k], GCD[k, a[[-1]]] == 1, IntersectingQ[m, IntegerDigits[k]]], k++]; AppendTo[a, k]; Set[m, IntegerDigits[k]], {i, 74}]; a] (* Michael De Vlieger, Mar 11 2021 *)
from sympy import factorint
def aupton(terms):
alst, aset = [1], {1}
for n in range(2, terms+1):
an = 1
anm1_digs, anm1_factors = set(str(alst[-1])), set(factorint(alst[-1]))
while True:
while an in aset: an += 1
if set(str(an)) & anm1_digs != set():
if set(factorint(an)) & anm1_factors == set():
alst.append(an); aset.add(an); break
an += 1
return alst
print(aupton(74)) # Michael S. Branicky, Mar 09 2021
a(16)=15 because GCD(a(16),a(15)) = GCD(15,21) = 3 and 1 is the common digit of 15 and 16.
S:= {2}:
A[1]:= 2:
L[1]:= {2}:
for n from 2 to 1000 do
k:= 0;
mS:= max(S);
Sp:= {$2..mS} minus S;
do
if Sp <> {} then
k:= min(Sp);
Sp:= Sp minus {k};
elif k < mS then k:= mS+1
else k:= k+1
fi;
if member(k,S) or igcd(k,A[n-1]) = 1 then next fi;
Lk:= convert(convert(k,base,10),set);
if Lk intersect L[n-1] <> {} then
A[n]:= k;
L[n]:= Lk;
S:= S union {k};
break
fi
od:
od:
seq(A[n],n=1..1000); # Robert Israel, Sep 07 2014
f[s_List]:=Block[{m=s[[-1]],k=2},While[MemberQ[s,k]||Intersection[IntegerDigits[k],IntegerDigits[m]]=={}||GCD[m,k]==1,k++];Append[s,k]];Nest[f,{2},71]
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