A283532 Primes p such that (q^2 - p^2) / 24 is prime, where q is the next prime after p.

7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 67, 83, 101, 109, 127, 131, 137, 251, 271, 281, 307, 331, 379, 383, 443, 487, 499, 563, 617, 641, 769, 821, 877, 937, 971, 1009, 1123, 1223, 1231, 1283, 1291, 1297, 1543, 1567, 1697, 1877, 2063, 2081, 2237, 2269, 2371, 2381, 2383, 2389, 2551, 2657, 2659, 2801, 2851, 2857

Offset: 1

Author

Thomas Ordowski and Altug Alkan, Mar 10 2017

Keywords

• nonn

Comments

This sequence is union of primes of the form:

6t-1 such that 6t+1 and t are both prime,

6t-1 such that 6t+5 and 3t+1 are both prime and 6t+1 is composite,

6t+1 such that 6t+5 and 2t+1 are both prime,

6t+1 such that 6t+7 and 3t+2 are both prime and 6t+5 is composite.

Examples

			7 is a term since 11 is the next prime and (11^2 - 7^2)/24 = 3 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

A060213 is a subsequence.

Cf. A075888.

Programs

Maple

N:= 10000: # to get all terms <= N
Primes:= select(isprime, [seq(i,i=3..N,2)]):
f:= proc(p,q)
  local r;
  r:= (q^2-p^2)/24;
  if r::integer and isprime(r) then p fi
end proc:
seq(f(Primes[i],Primes[i+1]),i=1..nops(Primes)-1); # Robert Israel, Mar 10 2017

Mathematica

Select[Prime@ Range@ 415, PrimeQ[(NextPrime[#]^2 - #^2)/24] &] (* Michael De Vlieger, Mar 13 2017 *)

PARI

is(n) = n>3 && isprime(n) && isprime((nextprime(n+1)^2-n^2)/24);