A358202 Lower twin primes p such that 6*p-1 and 6*p+1 are twin primes and (p+1)/6 is prime.

17, 137, 23537, 92957, 157217, 318677, 326657, 440177, 510617, 521537, 558497, 577937, 617717, 651017, 661097, 861437, 969257, 1093997, 1152077, 1168337, 1177157, 1260317, 1299917, 1356077, 1463177, 1514657, 1600097, 1617437, 1768757, 1773977, 1957937, 2065577, 2271497, 2335637, 2382557, 2450597

Offset: 1

Author

J. M. Bergot and Robert Israel, Nov 03 2022

Keywords

• nonn

Examples

			a(2) = 137 is a term because 137 and 139 are twin primes, 6*137-1 = 821 and 6*137+1 = 823 are twin primes, and (137+1)/6 = 23 is a prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Intersection of A060213 and A176131.

Programs

Maple

P:= select(isprime, {seq(i,i=5..2*10^7,2)}):
T:= P intersect map(`-`,P,2):
R:=T intersect map(t -> (t+1)/6, T):
sort(convert(select(t -> isprime((t+1)/6), R),list));

Mathematica

Select[Prime[Range[180000]], PrimeQ[# + 2] && PrimeQ[6*# - 1] && PrimeQ[6*# + 1] && PrimeQ[(# + 1)/6] &] (* Amiram Eldar, Nov 03 2022 *)
Select[Prime[Range[180000]],AllTrue[{#+2,6#+1,6#-1,(#+1)/6},PrimeQ]&] (* Harvey P. Dale, Jan 29 2023 *)