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

Author

Juri-Stepan Gerasimov, Mar 25 2024

Keywords

• nonn

Comments

Conjecture: this sequence is infinite.

Examples

			1 is this sequence because 27*1^3 + 3*1 = 30 has 2 prime neighbors 29 and 31.
		

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.

Programs

Magma

[m: m in [1..1500] | IsPrime(27*m^3+3*m-1) and IsPrime(27*m^3+3*m+1)];

Mathematica

Select[Range[1500], And @@ PrimeQ[27*#^3 + 3*# + {-1, 1}] &] (* Amiram Eldar, Mar 26 2024 *)