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 1-3 of 3 results.

A158722 Primes p which are not in A158720 and A158721.

Original entry on oeis.org

3, 7, 11, 19, 29, 37, 41, 43, 47, 61, 71, 79, 83, 89, 97, 101, 107, 109, 127, 131, 137, 139, 151, 157, 163, 173, 191, 199, 223, 227, 229, 239, 241, 251, 257, 263, 271, 277, 281, 283, 293, 311, 313, 317, 331, 349, 353, 367, 373, 379, 383, 389, 397, 401, 409, 419
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 24 2009

Keywords

Crossrefs

Cf. A158708, A158709, A158710, A158711, A158712, A158713, A158714, A158719, A158720, A158721

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[ !PrimeQ[Floor[p/3]+p]&&!PrimeQ[Ceiling[p/3]+p],AppendTo[lst,p]],{n,5!}];lst

A270384 Primes p such that (3/4)(p + 1) - 1 is also prime.

Original entry on oeis.org

3, 7, 23, 31, 71, 79, 151, 199, 223, 239, 263, 311, 359, 463, 479, 599, 743, 751, 823, 863, 911, 991, 1031, 1063, 1103, 1151, 1303, 1399, 1471, 1583, 1759, 1823, 1831, 1879, 1999, 2111, 2143, 2311, 2383, 2503, 2543, 2551, 2663, 2671, 2719, 3023, 3079, 3119, 3191, 3391, 3511
Offset: 1

Views

Author

Alonso del Arte, Mar 15 2016

Keywords

Comments

Set q = (3/4)(p + 1) - 1, then (q + 1)/(p + 1) = 3/4. If this sequence is proved to be infinite, that would prove two specific cases of the Schinzel-Sierpiński conjecture regarding rational numbers.
In fact this sequence is infinite under ('merely') Dickson's conjecture, as it requires infinitely many n with 3n + 2 and 4n + 3 both prime. - Charles R Greathouse IV, Apr 01 2016

Examples

			3 is in the sequence because 3/4 * 4 - 1 = 2, which is also prime.
7 is in the sequence because 3/4 * 8 - 1 = 5, which is also prime.
11 is not in the sequence because 3/4 * 12 - 1 = 8 = 2^3.

Links

Crossrefs

Cf. A158721.

Programs

  • Mathematica
    Select[Prime[Range[500]], PrimeQ[(3/4)(# + 1) - 1] &]
  • PARI
    is(n)=n%4==3 && isprime(n\4*3+2) && isprime(n) \\ Charles R Greathouse IV, Apr 01 2016

A158723 Greater of twin primes in A158720.

Original entry on oeis.org

13, 31, 73, 103, 181, 193, 433, 463, 571, 643, 661, 823, 1021, 1291, 1621, 1723, 2083, 2143, 2341, 2593, 2713, 3001, 3253, 3331, 3361, 3541, 4231, 4243, 4423, 4933, 5233, 5653, 5881, 6553, 6571, 6781, 6871, 6961, 7951, 8293, 9283, 9343, 9433, 9631, 9931
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Mar 24 2009

Keywords

Comments

If prime number from sequence A158720 is twin prime, it always (?) Greater of twin primes, and none (?) of Lesser of twin primes.

Crossrefs

Cf. A158708, A158709, A158710, A158711, A158712, A158713, A158714, A158719, A158720, A158721, A158722

Programs

  • Mathematica
    lst={};Do[p=Prime[n];If[PrimeQ[Floor[p/3]+p],If[PrimeQ[p-2],AppendTo[lst,p]]],{n,7!}];lst
Showing 1-3 of 3 results.

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

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