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: Paul Bourdelais

Paul Bourdelais's wiki page.

Paul Bourdelais has authored 18 sequences. Here are the ten most recent ones:

A366680 Numbers k such that (34^k + 1)/35 is prime.

Original entry on oeis.org

3, 294277, 735439
Offset: 1

Author

Paul Bourdelais, Oct 16 2023

Keywords

Comments

These are the repunits in base -34.

Examples

			3 is a term since (34^3 + 1)/35 = 1123 is a prime.
		

Crossrefs

Cf. A185230.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ (34^n+1)/35], Print[n]], {n, 0, 18000}]
  • PARI
    is(n) = my(q=(34^n+1)/35); (denominator(q)==1) && ispseudoprime(q);

A350036 Numbers k such that (81^k + 1)/82 is prime.

Original entry on oeis.org

3, 5, 701, 829, 1031, 1033, 7229, 19463, 370421
Offset: 1

Author

Paul Bourdelais, Dec 09 2021

Keywords

Comments

These are the Repunits in base -81. Since 81=3^4, factors will be of the form p=8nk+1. (Negative) bases that are powers of small numbers appear to have a higher frequency of primes than Repunits in other bases. The best linear fit for this base is currently 0.29918 which is much lower (better) than the conjectured 0.56145948 (see link to conjecture).

Examples

			3 is a term since (81^3 + 1)/82 = 6481 is a prime.
		

Programs

  • Mathematica
    Do[ If[ PrimeQ[ (81^n+1)/82], Print[n]], {n, 0, 1000000}]
  • PARI
    is(n)=isprime((81^n+1)/82)

A348170 Numbers k such that (35^k - 1)/34 is prime.

Original entry on oeis.org

313, 1297, 568453
Offset: 1

Author

Paul Bourdelais, Oct 04 2021

Keywords

Comments

These are the repunit primes in base 35.

Examples

			313 is a term since (35^313 - 1)/34 is a prime. It has 482 digits in base 10.
		

Programs

  • Mathematica
    Do[ If[ PrimeQ[ (35^n-1)/34], Print[n]], {n, 0, 600000}]
  • PARI
    is(n)=isprime((35^n-1)/34)

A345402 Numbers k such that (42^k-1)/41 is prime.

Original entry on oeis.org

2, 1319, 337081
Offset: 1

Author

Paul Bourdelais, Sep 28 2021

Keywords

Comments

These are the repunit primes in base 42.

Examples

			2 is a member since (42^2-1)/41 = 43 is prime.
		

Crossrefs

Cf. A218745.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ (42^n-1)/41], Print[n]], {n, 2, 400000}]
  • PARI
    is(n)=isprime((42^n-1)/41)

A347138 Numbers k such that (100^k + 1)/101 is prime.

Original entry on oeis.org

3, 293, 461, 11867, 90089
Offset: 1

Author

Paul Bourdelais, Aug 19 2021

Keywords

Comments

These are the repunit primes in base -100. It is unusual to represent numbers in a negative base, but it follows the same formulation as any base: numbers are represented as a sum of powers in that base, i.e., a0*1 + a1*b^1 + a2*b^2 + a3*b^3 ... Since the base is negative, the terms will be alternating positive/negative. For repunits the coefficients are all ones so the sum reduces to 1 + b + b^2 + b^3 + ... + b^(k-1) = (b^k-1)/(b-1). Since b is negative and k is an odd prime, the sum equals (|b|^k+1)/(|b|+1). For k=3, the sum is 9901, which is prime. As with all repunits, we only need to PRP test the prime exponents. The factors of repunits base -100 will be of the form p=2*k*m+1 where m must be even, which is common for (negative) bases that are squares.

Examples

			3 is a term since (100^3 + 1)/101 = 9901 is a prime.
		

Programs

  • Mathematica
    Do[ If[ PrimeQ[ (100^n + 1)/101], Print[n]], {n, 0, 18000}]
  • PARI
    is(n)=isprime((100^n+1)/101)

A339922 Numbers k such that 20^k - 3 is prime.

Original entry on oeis.org

1, 2, 5, 7, 9, 11, 15, 37, 59, 119, 154, 439, 745, 799, 1260, 1444, 3306, 8890, 14604, 15869, 20195, 99055, 186554, 396120
Offset: 1

Author

Paul Bourdelais, Dec 23 2020

Keywords

Examples

			1 is a term since 20^1 - 3 = 17 is a prime.
		

Crossrefs

Cf. A339921.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 20^n - 3], Print[n]], {n, 0, 200000}]
  • PARI
    is(n)=isprime(20^n - 3)

Extensions

a(24) from Paul Bourdelais, Jan 28 2021

A339924 Numbers k such that 14^k - 3 is prime.

Original entry on oeis.org

1, 2, 3, 10, 18, 19, 27, 122, 184, 347, 448, 542, 1685, 5618, 6208, 9867, 25522, 37688, 47067, 79195, 114592, 251797
Offset: 1

Author

Paul Bourdelais, Dec 23 2020

Keywords

Examples

			1 is a term since 14^1 - 3 = 11 is a prime.
		

Crossrefs

Cf. A339923.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 14^n - 3], Print[n]], {n, 0, 300000}]
  • PARI
    is(n)=isprime(14^n - 3)

A339923 Numbers k such that 14^k + 3 is prime.

Original entry on oeis.org

1, 2, 9, 24, 42, 74, 221, 620, 14064, 36697, 152048, 384558
Offset: 1

Author

Paul Bourdelais, Dec 23 2020

Keywords

Examples

			1 is a term since 14^1 + 3 = 17 is a prime.
		

Crossrefs

Cf. A339924.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 14^n + 3], Print[n]], {n, 0, 200000}]
  • PARI
    is(n)=isprime(14^n + 3)

Extensions

a(12) corresponds to a probable prime discovered by Paul Bourdelais, Jan 06 2021

A339921 Numbers k such that 20^k + 3 is prime.

Original entry on oeis.org

1, 5, 7, 13, 15, 18, 22, 61, 85, 208, 271, 898, 2142, 2856, 4392, 17171, 74886, 78901, 271951, 326600
Offset: 1

Author

Paul Bourdelais, Dec 23 2020

Keywords

Examples

			1 is a term since 20^1 + 3 = 23 is a prime.
		

Crossrefs

Cf. A339922.

Programs

  • Mathematica
    Do[ If[ PrimeQ[ 20^n + 3], Print[n]], {n, 0, 100000}]
  • PARI
    is(n)=isprime(20^n + 3)

Extensions

a(19)-a(20) correspond to probable primes discovered by Paul Bourdelais, Jan 06 2021

A309533 Numbers k such that (144^k + 1)/145 is prime.

Original entry on oeis.org

23, 41, 317, 3371, 45259, 119671
Offset: 1

Author

Paul Bourdelais, Aug 06 2019

Keywords

Comments

The corresponding primes are terms of A059055. - Bernard Schott, Aug 09 2019

Programs

  • Mathematica
    Do[p=Prime[n]; If[PrimeQ[(144^p + 1)/145], Print[p]], {n, 1, 1000000}]
  • PARI
    is(n)=ispseudoprime((144^n+1)/145)