cp's OEIS Frontend

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.

Showing 1-10 of 16 results. Next

A107829 Indices of primes occurring in A107809.

Original entry on oeis.org

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

Views

Author

Zak Seidov, May 24 2005

Keywords

Crossrefs

Cf. A107801 - A107814, A107821, A107822, A107823, A107824, A107825, A107826, A107827, A107828, A107830, A107831, A107832, A107833, A107834.

Formula

A107829(n) = pi(A107809(n)).

A107801 a(1) = prime(1), 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

2, 23, 3, 13, 11, 17, 7, 37, 31, 19, 29, 59, 5, 53, 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. If it exists, N > 10^1000. - Charles R Greathouse IV, Jul 19 2011

Links

Crossrefs

Cf. A107353.
Other cases of seed: 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), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

  • Haskell
    import Data.List (intersect, delete)
a107801 n = a107801_list !! (n-1)
a107801_list = 2 : f 2 (tail a000040_list) where
   f x ps = g ps where
     g (q:qs) | null (show x `intersect` show q) = g qs
              | otherwise                        = q : f q (delete q ps)
-- Reinhard Zumkeller, Mar 31 2012
  • Mathematica
    p=Prime[1];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=[2]); 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 19 2011
For n>=29, A(107800+i)(n) = A(107800+j)(n), 1 <= i < j <= 14. - Vladimir Shevelev, Mar 18 2012

A107814 a(1) = prime(14), 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

43, 3, 13, 11, 17, 7, 37, 23, 2, 29, 19, 31, 41, 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

Links

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), A107813 (a(1) = 41).

Programs

  • Maple
    Cands:= subsop(14=NULL, [seq(ithprime(i),i=1..1000)]):
S:= map(t -> convert(convert(t,base,10),set), Cands):
R:= 43: x:= 43: xs:= {3,4}:
for n from 2 to 100 do
  found:= false;
  for i from 1 do
    if S[i] intersect xs <> {} then
      R:= R, Cands[i];
      x:= Cands[i];
      xs:= S[i];
      Cands:= subsop(i=NULL,Cands);
      S:= subsop(i=NULL,S);
      found:= true;
      break
    fi
  od;
  if not found then break fi;
od:
R; # Robert Israel, Dec 16 2024
  • Mathematica
    p=Prime[14];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

Formula

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

A107802 a(1) = prime(2), 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

3, 13, 11, 17, 7, 37, 23, 2, 29, 19, 31, 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 & 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), 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), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

  • Mathematica
    p=Prime[2];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=[3]); 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

A107803 a(1) = prime(3), 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

5, 53, 3, 13, 11, 17, 7, 37, 23, 2, 29, 19, 31, 41, 43, 47, 67, 61, 71, 73, 79, 59, 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), 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), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

  • Mathematica
    p=Prime[3];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=[5]); 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

A107804 a(1) = prime(4), 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

7, 17, 11, 13, 3, 23, 2, 29, 19, 31, 37, 43, 41, 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 & 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), 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), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

  • Mathematica
    p=Prime[4];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=[7]); 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

A107805 a(1) = prime(5), 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

11, 13, 3, 23, 2, 29, 19, 17, 7, 37, 31, 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 & 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), 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), A107813 (a(1) = 41), A107814 (a(1) = 43).

Programs

  • Mathematica
    p=Prime[5];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=[11]); 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

A107806 a(1) = prime(6), 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

13, 3, 23, 2, 29, 19, 11, 17, 7, 37, 31, 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 & 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), A107807 (a(1) = 17), A107808 (a(1) = 19), 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[6];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=[13]); 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

A107807 a(1) = prime(7), 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

17, 7, 37, 3, 13, 11, 19, 29, 2, 23, 31, 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 & 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), A107808 (a(1) = 19), 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[7];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=[17]); 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

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
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