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

1,1

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.

Links

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

Example

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

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 *)

Prog

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

Crossrefs

A060213 is a subsequence.

Cf. A075888.

Sequence in context: A020633 A078873 A020603 * A163648 A135776 A067831

Adjacent sequences: A283529 A283530 A283531 * A283533 A283534 A283535

Keyword

nonn

Author

Thomas Ordowski and Altug Alkan, Mar 10 2017

Status

approved