cp's OEIS Frontend

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

%I A358202 #16 Jan 29 2023 17:30:38
%S A358202 17,137,23537,92957,157217,318677,326657,440177,510617,521537,558497,
%T A358202 577937,617717,651017,661097,861437,969257,1093997,1152077,1168337,
%U A358202 1177157,1260317,1299917,1356077,1463177,1514657,1600097,1617437,1768757,1773977,1957937,2065577,2271497,2335637,2382557,2450597
%N A358202 Lower twin primes p such that 6*p-1 and 6*p+1 are twin primes and (p+1)/6 is prime.
%H A358202 Robert Israel, <a href="/A358202/b358202.txt">Table of n, a(n) for n = 1..1000</a>
%e A358202 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.
%p A358202 P:= select(isprime, {seq(i,i=5..2*10^7,2)}):
%p A358202 T:= P intersect map(`-`,P,2):
%p A358202 R:=T intersect map(t -> (t+1)/6, T):
%p A358202 sort(convert(select(t -> isprime((t+1)/6), R),list));
%t A358202 Select[Prime[Range[180000]], PrimeQ[# + 2] && PrimeQ[6*# - 1] && PrimeQ[6*# + 1] && PrimeQ[(# + 1)/6] &] (* _Amiram Eldar_, Nov 03 2022 *)
%t A358202 Select[Prime[Range[180000]],AllTrue[{#+2,6#+1,6#-1,(#+1)/6},PrimeQ]&] (* _Harvey P. Dale_, Jan 29 2023 *)
%Y A358202 Intersection of A060213 and A176131.
%K A358202 nonn
%O A358202 1,1
%A A358202 _J. M. Bergot_ and _Robert Israel_, Nov 03 2022