|
|
A349666
|
|
Primes of the form 4*k+3 that are still a prime of the form 4*k+3 after 2 Collatz steps.
|
|
2
|
|
|
7, 31, 47, 71, 127, 151, 167, 239, 311, 431, 439, 479, 607, 631, 647, 727, 839, 911, 967, 991, 1039, 1231, 1319, 1399, 1471, 1511, 1559, 1567, 1607, 1879, 1951, 1999, 2111, 2239, 2311, 2351, 2447, 2671, 2719, 2927, 3119, 3167, 3191, 3359, 3391, 3671, 3727, 3767, 3911
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The two Collatz steps are 3*x + 1 and x/2.
Terms are primes in A002145 which after 2 Collatz iterations are still a prime in A002145.
Pythagorean primes (A002144), which are of the form 4*k+1, never produce any prime after those 2 steps. But further reducing by 2 produces primes in A349667.
Apparently this is a subsequence of A158709.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
(31*3 + 1)/2 = 47. Both 31 and 47 are primes of the form 4*k+3. Thus 31 is a term.
|
|
MATHEMATICA
|
Select[4*Range[0, 1000] + 3, PrimeQ[#] && Mod[(q = (3*# + 1)/2), 4] == 3 && PrimeQ[q] &] (* Amiram Eldar, Dec 24 2021 *)
|
|
PROG
|
(PARI) isok(p) = isprime(p) && ((p%4)==3) && isprime(q=(3*p+1)/2) && ((q%4)==3); \\ Michel Marcus, Dec 23 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|