A395198 Numbers k such that 2*k +- 1 and 5*k +- 1 are twin prime pairs.

6, 30, 36, 54, 114, 120, 210, 510, 546, 660, 804, 810, 1056, 1170, 1356, 1686, 1764, 1884, 1926, 2394, 3066, 3330, 3396, 4110, 4884, 5034, 5250, 6054, 8514, 9024, 9270, 9540, 10374, 11646, 11844, 13350, 13764, 14310, 14376, 15756, 16470, 16644, 17424, 17526, 18906, 21420, 21894, 23154, 23220, 24204

Offset

1,1

Comments

All terms are divisible by 6.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(5) = 114 is a term because 2*114-1 = 227, 2*114+1 = 229, 5*114-1 = 569 and 5*114+1 = 571 are all prime.

Maple

filter:= proc(n) andmap(isprime, [2*n-1, 2*n+1, 5*n-1, 5*n+1]) end proc:
select(filter, [seq(i, i = 6..30000, 6)]);

Mathematica

Select[Range[6, 30000, 6], AllTrue[{2*#-1, 2*#+1, 5*#-1, 5*#+1}, PrimeQ] &] (* Paolo Xausa, Apr 21 2026 *)

Prog

(PARI) first(nn)= my(r=List()); forstep(t=6, oo, 6, if(isprime(2*t-1) && isprime(5*t-1) && isprime(2*t+1) && isprime(5*t+1), listput(~r, t); #r<nn || break)); Vec(r); \\ Ruud H.G. van Tol, Apr 21 2026

Crossrefs

Intersection of A040040 and A153877.

Sequence in context: A397340 A197880 A175497 * A161812 A282944 A188062

Adjacent sequences: A395195 A395196 A395197 * A395199 A395200 A395201

Keyword

nonn

Author

Will Gosnell and Robert Israel, Apr 15 2026

Status

approved