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.

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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

A107833 Indices of primes occurring in A107813.

Original entry on oeis.org

13, 5, 6, 2, 9, 1, 10, 8, 7, 4, 12, 11, 14, 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, A107829, A107830, A107831, A107832, A107834.

Formula

A107833(n)=pi(A107813(n))

A107834 Indices of primes occurring in A107814.

Original entry on oeis.org

14, 2, 6, 5, 7, 4, 12, 9, 1, 10, 8, 11, 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 - A107833.

Formula

A107834(n)=pi(A107814(n))

A107822 Indices of primes occurring in A107802.

Original entry on oeis.org

2, 6, 5, 7, 4, 12, 9, 1, 10, 8, 11, 13, 14, 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, A107823, A107824, A107825, A107826, A107827, A107828, A107829, A107830, A107831, A107832, A107833, A107834.

Formula

A107822(n)=pi(A107802(n))

A107823 Indices of primes occurring in A107803.

Original entry on oeis.org

3, 16, 2, 6, 5, 7, 4, 12, 9, 1, 10, 8, 11, 13, 14, 15, 19, 18, 20, 21, 22, 17, 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, A107824, A107825, A107826, A107827, A107828, A107829, A107830, A107831, A107832, A107833, A107834.

Formula

A107823(n)=pi(A107803(n))

A107824 Indices of primes occurring in A107804.

Original entry on oeis.org

4, 7, 5, 6, 2, 9, 1, 10, 8, 11, 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, A107825, A107826, A107827, A107828, A107829, A107830, A107831, A107832, A107833, A107834.

Formula

A107824(n)=pi(A107804(n))

A107825 Indices of primes occurring in A107805.

Original entry on oeis.org

5, 6, 2, 9, 1, 10, 8, 7, 4, 12, 11, 13, 14, 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, A107826, A107827, A107828, A107829, A107830, A107831, A107832, A107833, A107834.

Formula

A107825(n)=pi(A107805(n))
Previous Showing 11-20 of 31 results. Next

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