A334026 - OEIS

%I #10 Jan 17 2021 19:01:41

%S 2,3,5,7,11,37,41,53,79,83,97,131,139,173,199,281,293,307,431,499,577,

%T 593,619,683,727,743,911,997,1013,1297,1429,1481,1511,1811,1901,1931,

%U 2003,2029,2141,2273,2351,2693,3037,3067,3109,3491,3499,3739,3769,3863,3911,4211,4373,4447,4481,4567,4871

%N Primes p such that 2*p and 4*p are 1 away from a prime.

%C Primes p such that at least one of 2*p-1 and 2*p+1 is prime, and at least one of 4*p-1 and 4*p+1 is prime.

%C Primes p such that either 2*p-1 and 4*p+1 are prime, or 2*p+1 and 4*p-1 are prime.

%C Primes p such that 4*p is in A333197.

%H Robert Israel, <a href="/A334026/b334026.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 5 is a member because 5, 2*5+1=11 and 4*5-1=19 are primes.

%p filter:= proc(t) isprime(t) and (isprime(2*t+1) or isprime(2*t-1)) and (isprime(4*t+1) or isprime(4*t-1)) end proc:

%p select(filter, [2,seq(i,i=3..10000,2)]);

%t Select[Prime[Range[700]],AnyTrue[2#+{1,-1},PrimeQ]&&AnyTrue[4#+{1,-1},PrimeQ] &] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jan 17 2021 *)

%Y Cf. A120628, A333197.

%K nonn

%O 1,1

%A _Robert Israel_, Apr 12 2020