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.

User: Henryk Dabrowski

Henryk Dabrowski's wiki page.

Henryk Dabrowski has authored 21 sequences. Here are the ten most recent ones:

A215970 Number of primes of the form 1 + b^65536 for 1 < b < 10^n.

Original entry on oeis.org

0, 0, 0, 0, 1, 14, 28
Offset: 1

Views

Author

Henryk Dabrowski, Aug 29 2012

Keywords

Comments

Primes 1 + b^65536 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.000170833*li(10^n)

Examples

			a(5) = 1 because the generalized Fermat numbers F_16(b) where b<10^5 are prime only for b = 48594.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698, A215699, A215700.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^65536+1))

A215969 Number of primes of the form 1 + b^32768 for 1 < b < 10^n.

Original entry on oeis.org

0, 0, 0, 0, 1, 16, 64
Offset: 1

Views

Author

Henryk Dabrowski, Aug 29 2012

Keywords

Comments

Primes 1 + b^32768 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.000177083*li(10^n)

Examples

			a(5) = 1 because the generalized Fermat numbers F_15(b) where b<10^5 are prime only for b = 70906.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698, A215699, A215700.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^32768 + 1))

A215962 Number of primes of the form 1 + b^16384 for 1 < b < 10^n.

Original entry on oeis.org

0, 0, 0, 0, 1, 33, 137
Offset: 1

Views

Author

Henryk Dabrowski, Aug 29 2012

Keywords

Comments

Primes 1 + b^16384 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.000488872*li(10^n)

Examples

			a(5) = 1 because the generalized Fermat numbers F_14(b) where b<10^5 are prime only for b = 67234.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698, A215699, A215700.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^16384+1))

A215961 Number of primes of the form 1 + b^8192 for 1 < b < 10^n.

Original entry on oeis.org

0, 0, 0, 0, 3, 74, 621
Offset: 1

Views

Author

Henryk Dabrowski, Aug 29 2012

Keywords

Comments

Primes 1 + b^8192 are a form of generalized Fermat primes. It is conjectured that a(n) is asymptotic to 0.00103368*li(10^n).

Examples

			a(5) = 3 because the generalized Fermat numbers F_13(b) where b<10^5 are prime only for b = 30406, 71852, 85654.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698, A215699, A215700.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^8192+1))

A215702 Number of primes of the form 1 + b^4096 for 1 < b < 10^n.

Original entry on oeis.org

0, 0, 0, 2, 16, 170
Offset: 1

Views

Author

Henryk Dabrowski, Aug 21 2012

Keywords

Comments

Primes 1 + b^4096 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.00205697*li(10^n)

Examples

			a(4) = 2 because the generalized Fermat numbers F_12(b) where b<10^4 are prime only for b = 1534, 7316.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^4096+1))

A215701 Number of primes of the form 1 + b^2048 for 1 < b < 10^n.

Original entry on oeis.org

0, 0, 1, 4, 40, 276
Offset: 1

Views

Author

Henryk Dabrowski, Aug 21 2012

Keywords

Comments

Primes 1 + b^2048 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.00352764*li(10^n)

Examples

			a(4) = 4 because the generalized Fermat numbers F_11(b) where b<10^4 are prime only for b = 150, 2558, 4650, 4772.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^2048+1))

A215700 Number of primes of the form 1 + b^1024 for 1 < b < 10^n.

Original entry on oeis.org

0, 0, 1, 14, 81, 578
Offset: 1

Views

Author

Henryk Dabrowski, Aug 21 2012

Keywords

Comments

Primes 1 + b^1024 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.00783139*li(10^n)

Examples

			a(3) = 1 because the generalized Fermat numbers F_10(b) where b<10^3 are prime only for b = 824.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^1024+1))

A215699 Number of primes of the form 1 + b^512 for 1 < b < 10^n.

Original entry on oeis.org

0, 1, 1, 28, 160, 1247
Offset: 1

Views

Author

Henryk Dabrowski, Aug 21 2012

Keywords

Comments

Primes 1 + b^512 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.0146271*li(10^n)

Examples

			a(3) = 1 because the generalized Fermat numbers F_9(b) where b<10^3 are prime only for b = 46.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058, A215698.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^512+1))

A215698 Number of primes of the form 1 + b^256 for 1 < b < 10^n.

Original entry on oeis.org

0, 0, 4, 30, 272, 2322
Offset: 1

Views

Author

Henryk Dabrowski, Aug 21 2012

Keywords

Comments

Primes 1 + b^256 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.0290422*li(10^n)

Examples

			a(3) = 4 because the generalized Fermat numbers F_8(b) where b<10^3 are prime only for b: 278, 614, 892, 898.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057, A215058.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^256+1))

A215058 Number of primes of the form 1 + b^128 for 1 < b < 10^n.

Original entry on oeis.org

0, 0, 7, 25, 242, 1933, 16080, 139921, 1234958
Offset: 1

Views

Author

Henryk Dabrowski, Aug 01 2012

Keywords

Comments

Primes 1 + b^128 are a form of generalized Fermat primes.
It is conjectured that a(n) is asymptotic to 0.0242888*li(10^n)

Examples

			a(3) = 7 because the generalized Fermat numbers F_7(b) where b<10^3 are prime only for b: 120, 190, 234, 506, 532, 548, 960.

Links

Crossrefs

Cf. A215047, A215048, A215049, A215050, A215051, A215057.

Programs

  • PARI
    a(n) = sum(b=1, 10^n/2-1, isprime((2*b)^128+1))

Extensions

a(8)-a(9) from Kellen Shenton, Aug 10 2020

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