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A089528 Primes p of the form 2*prime(k) + 3 such that 2*prime(k+1) + 3 is the next prime after p.

%I A089528 #13 Dec 14 2021 15:20:50
%S A089528 13,37,89,277,389,397,449,457,701,761,929,2069,2221,2609,2857,3121,
%T A089528 3217,3221,6329,7229,7537,7649,8581,8677,9277,9941,11317,11681,12401,
%U A089528 13421,13469,15649,16729,17401,17497,17729,18257,19289,19489,19937,20509
%N A089528 Primes p of the form 2*prime(k) + 3 such that 2*prime(k+1) + 3 is the next prime after p.
%H A089528 Harvey P. Dale, <a href="/A089528/b089528.txt">Table of n, a(n) for n = 1..1000</a>
%F A089528 a(n) = 2*A089527(n) + 3 = 2*A000040(A089526(n)) + 3 = A000040(A089529(n)).
%e A089528 p(3)=5, 2*5 + 3 = 13 = p(6);
%e A089528 p(4)=7, 2*7 + 3 = 17 = p(7).
%t A089528 Select[Partition[2#+3&/@Prime[Range[2500]],2,1],AllTrue[#,PrimeQ] && NextPrime[ #[[1]]]==#[[2]]&][[All,1]] (* _Harvey P. Dale_, Dec 14 2021 *)
%o A089528 (PARI) forprime(p=2,10500,my(p23=2*p+3);if(isprime(p23),my(pp=2*nextprime(p+1)+3);if(isprime(pp)&&pp==nextprime(p23+1),print1(p23,", ")))) \\ _Hugo Pfoertner_, Aug 04 2021
%Y A089528 Subsequence of A089531.
%Y A089528 Cf. A089526, A089527, A089529.
%K A089528 nonn
%O A089528 1,1
%A A089528 _Ray Chandler_, Nov 07 2003
%E A089528 Offset changed to 1 by _Jinyuan Wang_, Aug 04 2021