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

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

1,1

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Example

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.

Mathematica

Select[Prime[Range[500]], PrimeQ[(3/4)(# + 1) - 1] &]

Prog

(PARI) is(n)=n%4==3 && isprime(n\4*3+2) && isprime(n) \\ Charles R Greathouse IV, Apr 01 2016

Crossrefs

Cf. A158721.

Sequence in context: A187222 A122094 A260350 * A213897 A291776 A135570

Adjacent sequences: A270381 A270382 A270383 * A270385 A270386 A270387

Keyword

nonn

Author

Alonso del Arte, Mar 15 2016

Status

approved