

A283532


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


2



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
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OFFSET

1,1


COMMENTS

This sequence is union of primes of the form:
6t1 such that 6t+1 and t are both prime,
6t1 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



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^2p^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)^2n^2)/24);


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



