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 1-4 of 4 results.

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))

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))

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))

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))
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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