A371029 Numbers m such that if k = 27*m^3 + 3*m then k-1 and k+1 are primes.

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

Offset

1,2

Comments

Conjecture: this sequence is infinite.

Links

Table of n, a(n) for n=1..60.

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.

Cf. A008585, A014574.

Sequence in context: A067531 A031029 A134985 * A111018 A326132 A342630

Adjacent sequences: A371026 A371027 A371028 * A371030 A371031 A371032

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 25 2024

Status

approved