|
|
A236484
|
|
Primes p with p + 2, prime(p) + 2, prime(prime(p)) + 2, prime(prime(prime(p))) + 2, prime(prime(prime(prime(p)))) + 2 all prime.
|
|
4
|
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
By the general conjecture in A236481, this sequence should have infinitely many terms.
|
|
LINKS
|
|
|
EXAMPLE
|
a(1) = 2371709 with 2371709, 2371709 + 2 = 2371711, prime(2371709) + 2 = 38917889 + 2 = 38917891, prime(38917889) + 2 = 754394519 + 2 = 754394521, prime(754394519) + 2 = 16978533527 + 2 = 16978533529 and prime(16978533527) + 2 = 437397516929 + 2 = 437397516931 all prime.
|
|
MATHEMATICA
|
p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[Prime[n]+2]&&PrimeQ[Prime[Prime[n]]+2]&&PrimeQ[Prime[Prime[Prime[n]]]+2]&&PrimeQ[Prime[Prime[Prime[Prime[n]]]]+2]
n=0; Do[If[p[Prime[m]], n=n+1; Print[n, " ", Prime[m]]], {m, 1, 10^7}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|