OFFSET
1,2
COMMENTS
Sierpiński proved that under Schinzel's hypothesis H this sequence is infinite.
Sierpiński showed that the only quadruple of consecutive primes of the form (2k+1)^2 - 2 are for k = 1 (i.e., 1 and 2 are the only consecutive terms in this sequence).
Numbers k such that the 3 consecutive integers k, k+1 and k+2 belong to A088572. - Michel Marcus, Oct 13 2017
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Wacław Sierpiński, Remarque sur la distribution de nombres premiers, Matematički Vesnik, Vol. 2(17), Issue 31 (1965), pp. 77-78.
Eric Weisstein's World of Mathematics, Near-Square Prime.
Wikipedia, Schinzel's hypothesis H.
EXAMPLE
The first triples are: k = 1: (7, 23, 47), k = 2: (23, 47, 79), k = 16: (1087, 1223, 1367).
MATHEMATICA
Select[Range[10^4], AllTrue[{(2#+1)^2-2, (2#+3)^2-2, (2#+5)^2-2}, PrimeQ] &]
PROG
(PARI) f(n) = 4*n^2 + 4*n - 1;
isok(n) = isprime(f(n)) && isprime(f(n+1)) && isprime(f(n+2)); \\ Michel Marcus, Oct 13 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Oct 13 2017
STATUS
approved