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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.

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A107808 a(1) = prime(8), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

Original entry on oeis.org

19, 11, 13, 3, 23, 2, 29, 59, 5, 53, 31, 17, 7, 37, 43, 41, 47, 67, 61, 71, 73, 79, 89, 83, 103, 101, 107, 97, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
Offset: 1

Views

Author

Zak Seidov & Eric Angelini, May 24 2005

Keywords

Comments

a(n) = prime(n) for almost all n. Probably a(n) = prime(n) for all n > N for some N, but N must be very large. - Charles R Greathouse IV, Jul 20 2011

Crossrefs

Cf. A107353.
Other cases of seed: A107801 (a(1) = 2), A107802 (a(1) = 3), A107803 (a(1) = 5), A107804 (a(1) = 7), A107805 (a(1) = 11), A107806 (a(1) = 13), A107807 (a(1) = 17), A107809 (a(1) = 23), A107810 (a(1) = 29), A107811 (a(1) = 31), A107812 (a(1) = 37), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

  • Mathematica
    p=Prime[8];b={p};d=p;Do[Do[r=Prime[c];If[FreeQ[b, r]&&Intersection@@IntegerDigits/@{d, r}=!={}, b=Append[b, r];d=r;Break[]], {c, 1000}], {k, 60}];b
  • PARI
    common(a,b)=a=vecsort(eval(Vec(Str(a))),,8);b=vecsort(eval(Vec(Str(b))),,8);#a+#b>#vecsort(concat(a,b),,8)
in(v,x)=for(i=1,#v,if(v[i]==x,return(1)));0
lista(nn) = {my(v=[19]); for(n=2, nn, forprime(p=2, default(primelimit), if(!in(v,p)&&common(v[#v],p), v=concat(v,p); break))); v; }
\\ Charles R Greathouse IV, Jul 20 2011

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jul 20 2011

A107810 a(1) = prime(10), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

Original entry on oeis.org

29, 2, 23, 3, 13, 11, 17, 7, 37, 31, 19, 41, 43, 47, 67, 61, 71, 73, 53, 5, 59, 79, 89, 83, 103, 101, 107, 97, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
Offset: 1

Views

Author

Zak Seidov and Eric Angelini, May 24 2005

Keywords

Comments

a(n) = prime(n) for almost all n. Probably a(n) = prime(n) for all n > N for some N, but N must be very large. - Charles R Greathouse IV, Jul 20 2011

Crossrefs

Cf. A107353.
Other cases of seed: A107801 (a(1) = 2), A107802 (a(1) = 3), A107803 (a(1) = 5), A107804 (a(1) = 7), A107805 (a(1) = 11), A107806 (a(1) = 13), A107807 (a(1) = 17), A107808 (a(1) = 19), A107809 (a(1) = 23), A107811 (a(1) = 31), A107812 (a(1) = 37), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

  • Mathematica
    p=Prime[10];b={p};d=p;Do[Do[r=Prime[c];If[FreeQ[b, r]&&Intersection@@IntegerDigits/@{d, r}=!={}, b=Append[b, r];d=r;Break[]], {c, 1000}], {k, 60}];b
  • PARI
    common(a,b)=a=vecsort(eval(Vec(Str(a))),,8);b=vecsort(eval(Vec(Str(b))),,8);#a+#b>#vecsort(concat(a,b),,8)
in(v,x)=for(i=1,#v,if(v[i]==x,return(1)));0
lista(nn) = {my(v=[29]); for(n=2, nn, forprime(p=2, default(primelimit), if(!in(v,p)&&common(v[#v],p), v=concat(v,p); break))); v; }
\\ Charles R Greathouse IV, Jul 20 2011

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jul 20 2011

A107811 a(1) = prime(11), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

Original entry on oeis.org

31, 3, 13, 11, 17, 7, 37, 23, 2, 29, 19, 41, 43, 47, 67, 61, 71, 73, 53, 5, 59, 79, 89, 83, 103, 101, 107, 97, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
Offset: 1

Views

Author

Zak Seidov and Eric Angelini, May 24 2005

Keywords

Comments

a(n) = prime(n) for almost all n. Probably a(n) = prime(n) for all n > N for some N, but N must be very large. - Charles R Greathouse IV, Jul 20 2011

Crossrefs

Cf. A107353.
Other cases of seed: A107801 (a(1) = 2), A107802 (a(1) = 3), A107803 (a(1) = 5), A107804 (a(1) = 7), A107805 (a(1) = 11), A107806 (a(1) = 13), A107807 (a(1) = 17), A107808 (a(1) = 19), A107809 (a(1) = 23), A107810 (a(1) = 29), A107812 (a(1) = 37), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

  • Mathematica
    p=Prime[11];b={p};d=p;Do[Do[r=Prime[c];If[FreeQ[b, r]&&Intersection@@IntegerDigits/@{d, r}=!={}, b=Append[b, r];d=r;Break[]], {c, 1000}], {k, 60}];b
  • PARI
    common(a,b)=a=vecsort(eval(Vec(Str(a))),,8);b=vecsort(eval(Vec(Str(b))),,8);#a+#b>#vecsort(concat(a,b),,8)
in(v,x)=for(i=1,#v,if(v[i]==x,return(1)));0
lista(nn) = {my(v=[31]); for(n=2, nn, forprime(p=2, default(primelimit), if(!in(v,p)&&common(v[#v],p), v=concat(v,p); break))); v; }
\\ Charles R Greathouse IV, Jul 20 2011

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jul 20 2011

A107812 a(1) = prime(12), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

Original entry on oeis.org

37, 3, 13, 11, 17, 7, 47, 41, 19, 29, 2, 23, 31, 43, 53, 5, 59, 79, 67, 61, 71, 73, 83, 89, 97, 107, 101, 103, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
Offset: 1

Views

Author

Zak Seidov and Eric Angelini, May 24 2005

Keywords

Comments

a(n) = prime(n) for almost all n. Probably a(n) = prime(n) for all n > N for some N, but N must be very large. - Charles R Greathouse IV, Jul 20 2011

Crossrefs

Cf. A107353.
Other cases of seed: A107801 (a(1) = 2), A107802 (a(1) = 3), A107803 (a(1) = 5), A107804 (a(1) = 7), A107805 (a(1) = 11), A107806 (a(1) = 13), A107807 (a(1) = 17), A107808 (a(1) = 19), A107809 (a(1) = 23), A107810 (a(1) = 29), A107811 (a(1) = 31), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

  • Mathematica
    p=Prime[12];b={p};d=p;Do[Do[r=Prime[c];If[FreeQ[b, r]&&Intersection@@IntegerDigits/@{d, r}=!={}, b=Append[b, r];d=r;Break[]], {c, 1000}], {k, 60}];b
  • PARI
    common(a,b)=a=vecsort(eval(Vec(Str(a))),,8);b=vecsort(eval(Vec(Str(b))),,8);#a+#b>#vecsort(concat(a,b),,8)
in(v,x)=for(i=1,#v,if(v[i]==x,return(1)));0
lista(nn) = {my(v=[37]); for(n=2, nn, forprime(p=2, default(primelimit), if(!in(v,p)&&common(v[#v],p), v=concat(v,p); break))); v; }
\\ Charles R Greathouse IV, Jul 20 2011

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jul 20 2011

A107813 a(1) = prime(13), for n >= 2, a(n) is the smallest prime not previously used which contains a digit from a(n-1).

Original entry on oeis.org

41, 11, 13, 3, 23, 2, 29, 19, 17, 7, 37, 31, 43, 47, 67, 61, 71, 73, 53, 5, 59, 79, 89, 83, 103, 101, 107, 97, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277
Offset: 1

Views

Author

Zak Seidov and Eric Angelini, May 24 2005

Keywords

Comments

a(n) = prime(n) for almost all n. Probably a(n) = prime(n) for all n > N for some N, but N must be very large. - Charles R Greathouse IV, Jul 20 2011

Crossrefs

Cf. A107353.
Other cases of seed: A107801 (a(1) = 2), A107802 (a(1) = 3), A107803 (a(1) = 5), A107804 (a(1) = 7), A107805 (a(1) = 11), A107806 (a(1) = 13), A107807 (a(1) = 17), A107808 (a(1) = 19), A107809 (a(1) = 23), A107810 (a(1) = 29), A107811 (a(1) = 31), A107812 (a(1) = 37), A107814 (a(1) = 43).

Programs

  • Mathematica
    p=Prime[13];b={p};d=p;Do[Do[r=Prime[c];If[FreeQ[b, r]&&Intersection@@IntegerDigits/@{d, r}=!={}, b=Append[b, r];d=r;Break[]], {c, 1000}], {k, 60}];b
  • PARI
    common(a,b)=a=vecsort(eval(Vec(Str(a))),,8);b=vecsort(eval(Vec(Str(b))),,8);#a+#b>#vecsort(concat(a,b),,8)
in(v,x)=for(i=1,#v,if(v[i]==x,return(1)));0
lista(nn) = {my(v=[41]); for(n=2, nn, forprime(p=2, default(primelimit), if(!in(v,p)&&common(v[#v],p), v=concat(v,p); break))); v; }
\\ Charles R Greathouse IV, Jul 20 2011

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jul 20 2011

A107778 a(1)=7, a(n) = smallest integer not previously used which contains a digit from a(n-1).

Original entry on oeis.org

7, 17, 1, 10, 0, 20, 2, 12, 11, 13, 3, 23, 21, 14, 4, 24, 22, 25, 5, 15, 16, 6, 26, 27, 28, 8, 18, 19, 9, 29, 32, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 40, 41, 42, 44, 45, 46, 47, 48, 49, 54, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 61, 62, 63, 64, 66, 67, 68, 69, 76, 70
Offset: 1

Views

Author

Eric Angelini & Zak Seidov, May 24 2005

Keywords

Comments

Cf. A107353 a(1)=0, A107772 a(1)=1, A107773 a(1)=2, A107774 a(1)=3, A107775 a(1)=4, A107776 a(1)=5, A107777 a(1)=6, A107779 a(1)=8, A107780 a(1)=9, A107781 a(1)=10

Links

Crossrefs

Cf. A107353, A107772, A107773, A107774, A107775, A107776, A107777, A107779, A107780, A107781.

Programs

  • Maple
    Agenda:= [$0..6,$8..100]: A[1]:= 7: S:= {7}:
for i from 2 do
  found:= false;
  for j from 1 to nops(Agenda) do
    r:= Agenda[j];
    Sr:= convert(convert(r,base,10),set);
    if Sr intersect S <> {} then
        A[i]:= r;
        Agenda:= subsop(j=NULL,Agenda);
        S:= Sr;
        found:= true;
        break
     fi
   od;
   if not found then break fi;
od:
seq(A[n],n=1..i-1); # Robert Israel, Jul 08 2019
  • Mathematica
    f[l_] := Block[{c = 0}, While[ MemberQ[l, c] || Intersection @@ IntegerDigits /@{Last[l], c}=={}, c++ ];Return[Append[l, c]]];Nest[f, {7}, 70] (* Ray Chandler, Jul 19 2005 *)

Formula

From Robert Israel, Jul 09 2019: (Start)
For n >= 29, it appears that a(n) = n-1 except:
a(i*10^k+j) = i*10^k+j-2 if i=1 and 2<=j<=10, or 2<=i<=8 and 2<=j<=i.
a(i*10^k+1) = i*10^k+i-1 for 2<=i<=8 or i=10.
(End)

A107780 a(1)=9, a(n) = smallest integer not previously used which contains a digit from a(n-1).

Original entry on oeis.org

9, 19, 1, 10, 0, 20, 2, 12, 11, 13, 3, 23, 21, 14, 4, 24, 22, 25, 5, 15, 16, 6, 26, 27, 7, 17, 18, 8, 28, 29, 32, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 40, 41, 42, 44, 45, 46, 47, 48, 49, 54, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 61, 62, 63, 64, 66, 67, 68, 69, 76, 70
Offset: 1

Views

Author

Eric Angelini & Zak Seidov, May 24 2005

Keywords

Links

Crossrefs

Cf. A107353 a(1)=0, A107772 a(1)=1, A107773 a(1)=2, A107774 a(1)=3, A107775 a(1)=4, A107776 a(1)=5, A107777 a(1)=6, A107778 a(1)=7, A107779 a(1)=8, A107781 a(1)=10.

Programs

  • Maple
    S:= [$0..100]:
Res:= 9: S:= subs(9=NULL,S):
digs:= {9}:
while S <> [] do
  found:= false;
  for i from 1 to nops(S) while not found do
    ndigs:= convert(convert(S[i],base,10),set);
    if ndigs intersect digs <> {} then
      found:= true;
      Res:=Res, S[i];
      S:= subsop(i=NULL, S);
      digs:= ndigs;
    fi
  od;
  if not found then break fi;
od:
Res; # Robert Israel, Jan 22 2020
  • Mathematica
    f[l_] := Block[{c = 0}, While[ MemberQ[l, c] || Intersection @@ IntegerDigits /@{Last[l], c}=={}, c++ ];Return[Append[l, c]]];Nest[f, {9}, 70] (* Ray Chandler, Jul 19 2005 *)

A107772 a(1)=1, a(n) = smallest integer not previously used which contains a digit from a(n-1).

Original entry on oeis.org

1, 10, 0, 20, 2, 12, 11, 13, 3, 23, 21, 14, 4, 24, 22, 25, 5, 15, 16, 6, 26, 27, 7, 17, 18, 8, 28, 29, 9, 19, 31, 30, 32, 33, 34, 35, 36, 37, 38, 39, 43, 40, 41, 42, 44, 45, 46, 47, 48, 49, 54, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 61, 62, 63, 64, 66, 67, 68, 69, 76, 70
Offset: 1

Views

Author

Eric Angelini & Zak Seidov, May 24 2005

Keywords

Comments

Cf. A107353 a(1)=0, A107773 a(1)=2, A107774 a(1)=3, A107775 a(1)=4, A107776 a(1)=5, A107777 a(1)=6, A107778 a(1)=7, A107779 a(1)=8, A107780 a(1)=9, A107781 a(1)=10

Crossrefs

Cf. A107353, A107773, A107774, A107775, A107776, A107777, A107778, A107779, A107780, A107781.

Programs

  • Mathematica
    f[l_] := Block[{c = 0}, While[ MemberQ[l, c] || Intersection @@ IntegerDigits /@{Last[l], c}=={}, c++ ];Return[Append[l, c]]];Nest[f, {1}, 70] (* Ray Chandler, Jul 19 2005 *)

A107773 a(1)=2, a(n) = smallest integer not previously used which contains a digit from a(n-1).

Original entry on oeis.org

2, 12, 1, 10, 0, 20, 21, 11, 13, 3, 23, 22, 24, 4, 14, 15, 5, 25, 26, 6, 16, 17, 7, 27, 28, 8, 18, 19, 9, 29, 32, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 40, 41, 42, 44, 45, 46, 47, 48, 49, 54, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 61, 62, 63, 64, 66, 67, 68, 69, 76, 70
Offset: 1

Views

Author

Eric Angelini & Zak Seidov, May 24 2005

Keywords

Comments

Cf. A107353 a(1)=0, A107772 a(1)=1, A107774 a(1)=3, A107775 a(1)=4, A107776 a(1)=5, A107777 a(1)=6, A107778 a(1)=7, A107779 a(1)=8, A107780 a(1)=9, A107781 a(1)=10

Crossrefs

Cf. A107353, A107772, A107774, A107775, A107776, A107777, A107778, A107779, A107780, A107781.

Programs

  • Mathematica
    f[l_] := Block[{c = 0}, While[ MemberQ[l, c] || Intersection @@ IntegerDigits /@{Last[l], c}=={}, c++ ];Return[Append[l, c]]];Nest[f, {2}, 70] (* Ray Chandler, Jul 19 2005 *)

A107774 a(1)=3, a(n) = smallest integer not previously used which contains a digit from a(n-1).

Original entry on oeis.org

3, 13, 1, 10, 0, 20, 2, 12, 11, 14, 4, 24, 21, 15, 5, 25, 22, 23, 26, 6, 16, 17, 7, 27, 28, 8, 18, 19, 9, 29, 32, 30, 31, 33, 34, 35, 36, 37, 38, 39, 43, 40, 41, 42, 44, 45, 46, 47, 48, 49, 54, 50, 51, 52, 53, 55, 56, 57, 58, 59, 65, 60, 61, 62, 63, 64, 66, 67, 68, 69, 76, 70
Offset: 1

Views

Author

Eric Angelini & Zak Seidov, May 24 2005

Keywords

Comments

Cf. A107353 a(1)=0, A107772 a(1)=1, A107773 a(1)=2, A107775 a(1)=4, A107776 a(1)=5, A107777 a(1)=6, A107778 a(1)=7, A107779 a(1)=8, A107780 a(1)=9, A107781 a(1)=10

Crossrefs

Cf. A107353, A107772, A107773, A107775, A107776, A107777, A107778, A107779, A107780, A107781.

Programs

  • Mathematica
    f[l_] := Block[{c = 0}, While[ MemberQ[l, c] || Intersection @@ IntegerDigits /@{Last[l], c}=={}, c++ ];Return[Append[l, c]]];Nest[f, {3}, 70] (* Ray Chandler, Jul 19 2005 *)
Previous Showing 11-20 of 35 results. Next

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