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

%I A283532 #27 Mar 13 2017 22:27:23
%S A283532 7,11,13,17,19,23,29,31,37,41,67,83,101,109,127,131,137,251,271,281,
%T A283532 307,331,379,383,443,487,499,563,617,641,769,821,877,937,971,1009,
%U A283532 1123,1223,1231,1283,1291,1297,1543,1567,1697,1877,2063,2081,2237,2269,2371,2381,2383,2389,2551,2657,2659,2801,2851,2857
%N A283532 Primes p such that (q^2 - p^2) / 24 is prime, where q is the next prime after p.
%C A283532 This sequence is union of primes of the form:
%C A283532 6t-1 such that 6t+1 and t are both prime,
%C A283532 6t-1 such that 6t+5 and 3t+1 are both prime and 6t+1 is composite,
%C A283532 6t+1 such that 6t+5 and 2t+1 are both prime,
%C A283532 6t+1 such that 6t+7 and 3t+2 are both prime and 6t+5 is composite.
%H A283532 Robert Israel, <a href="/A283532/b283532.txt">Table of n, a(n) for n = 1..10000</a>
%e A283532 7 is a term since 11 is the next prime and (11^2 - 7^2)/24 = 3 is prime.
%p A283532 N:= 10000: # to get all terms <= N
%p A283532 Primes:= select(isprime, [seq(i,i=3..N,2)]):
%p A283532 f:= proc(p,q)
%p A283532   local r;
%p A283532   r:= (q^2-p^2)/24;
%p A283532   if r::integer and isprime(r) then p fi
%p A283532 end proc:
%p A283532 seq(f(Primes[i],Primes[i+1]),i=1..nops(Primes)-1); # _Robert Israel_, Mar 10 2017
%t A283532 Select[Prime@ Range@ 415, PrimeQ[(NextPrime[#]^2 - #^2)/24] &] (* _Michael De Vlieger_, Mar 13 2017 *)
%o A283532 (PARI) is(n) = n>3 && isprime(n) && isprime((nextprime(n+1)^2-n^2)/24);
%Y A283532 A060213 is a subsequence.
%Y A283532 Cf. A075888.
%K A283532 nonn
%O A283532 1,1
%A A283532 _Thomas Ordowski_ and _Altug Alkan_, Mar 10 2017