Primes in n-fibonacci sequence and n-step fibonacci sequence

[sweety439]

The n-fibonacci primes are:

F(1,n) is (probable) prime: 3, 4, 5, 7, 11, 13, 17, 23, 29, 43, 47, 83, 131, 137, 359, 431, 433, 449, 509, 569, 571, 2971, 4723, 5387, 9311, 9677, 14431, 25561, 30757, 35999, 37511, 50833, 81839, 104911, 130021, 148091, 201107, 397379, 433781, 590041, 593689, 604711, 931517, 1049897, 1285607, 1636007, 1803059, 1968721, 2904353, ... (A001605)

F(2,n) is (probable) prime: 2, 3, 5, 11, 13, 29, 41, 53, 59, 89, 97, 101, 167, 181, 191, 523, 929, 1217, 1301, 1361, 2087, 2273, 2393, 8093, 13339, 14033, 23747, 28183, 34429, 36749, 90197, ... (A096650)

F(3,n) is (probable) prime: 2, 5, 11, 17, 61, 103, 167, 193, 293, 643, 647, 911, 11243, 29437, 55021, ... (A209493)

[sweety439]

Also, for n-Lucas prime:

L(1,n) is prime: 2, 4, 5, 7, 8, 11, 13, 16, 17, 19, 31, 37, 41, 47, 53, 61, 71, 79, 113, 313, 353, 503, 613, 617, 863, 1097, 1361, 4787, 4793, 5851, 7741, 8467, 10691, 12251, 13963, 14449, 19469, 35449, 36779, 44507, 51169, 56003, 81671, 89849, 94823, 140057, 148091, 159521, 183089, 193201, 202667, 344293, 387433, 443609, 532277, 574219, 616787, 631181, 637751, 651821, 692147, 901657, 1051849, ... (A001606)

L(2,n) is prime: 2, 3, 4, 5, 7, 8, 16, 19, 29, 47, 59, 163, 257, 421, 937, 947, 1493, 1901, 6689, 8087, 9679, 28753, 79043, 129127, 145969, 165799, 168677, 170413, 172243, ... (A099088)

[sweety439]

Originally Posted by sweety439

n-fibonacci sequence:

n OEIS sequence
1 A000045
2 A000129
3 A006190
4 A001076
5 A052918
6 A005668
7 A054413
8 A041025
9 A099371
10 A041041
11 A049666
12 A041061

n-step fibonacci sequence:

n OEIS sequence
1 A000012
2 A000045
3 A000213
4 A000288
5 A000322
6 A000383
7 A060455
8 A123526
9 A127193
10 A127194
11 A127624
12 A207539

Is there a project of searching primes in these sequences?

Another definition of n-step fibonacci sequence:

n OEIS sequence
1 A000012
2 A000045
3 A000073
4 A000078
5 A001591
6 A001592
7 A122189
8 A079262
9 A104144
10 A122265
11 A168082
12 A168083

[sweety439]

Also, for Lucas U(1,-n) sequences: (the n-fibonacci sequence is the Lucas (n,-1) sequence)

n OEIS sequence
1 A000045
2 A001045
3 A006130
4 A006131
5 A015440
6 A015441
7 A015442
8 A015443
9 A015445
10 A015446
11 A015447
12 A053404

[sweety439]

Is there a project of searching primes in these sequences?

[science_man_88]

okay so we have 0,1,1 for them all if continued backwards ( some sequences you link to don't have the 0). then forwards from that you have n+1, then you have 2n+1, then n^2+3n+1, then 3(n^2)+4n+1, etc. so you can check which have n that cause any primes >3 to possibly occur.

[Batalov]

Originally Posted by sweety439

Is there a project of searching primes in these sequences?

Prime Jacobsthal numbers (except 5) are Wagstaff primes.
There is a project searching for Wagstaff primes.