|
| |
|
|
A371029
|
|
Numbers m such that if k = 27*m^3 + 3*m then k-1 and k+1 are primes.
|
|
0
|
|
|
|
1, 5, 6, 7, 13, 29, 39, 40, 45, 81, 120, 122, 127, 142, 143, 205, 214, 241, 293, 334, 341, 390, 391, 408, 486, 502, 506, 510, 577, 632, 640, 655, 669, 675, 686, 711, 720, 792, 793, 794, 802, 851, 859, 891, 901, 909, 972, 974, 992, 1000, 1041, 1078, 1082, 1096, 1099, 1111, 1206, 1258, 1280, 1423
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Conjecture: this sequence is infinite.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
1 is this sequence because 27*1^3 + 3*1 = 30 has 2 prime neighbors 29 and 31.
|
|
|
MATHEMATICA
|
Select[Range[1500], And @@ PrimeQ[27*#^3 + 3*# + {-1, 1}] &] (* Amiram Eldar, Mar 26 2024 *)
|
|
|
PROG
|
(Magma) [m: m in [1..1500] | IsPrime(27*m^3+3*m-1) and IsPrime(27*m^3+3*m+1)];
|
|
|
CROSSREFS
|
Numbers m such that (n*m)^n + n*m has 2 prime neighbors: A040040 (n=1); no sequence (n=2) in OEIS; this sequence (n=3); no sequence (n=4) in OEIS.
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
