A089492 - OEIS

%I #8 Aug 06 2021 07:04:08

%S 1552237,4315469,8774137,9629197,10048081,10875149,11469389,14498741,

%T 18280861,18789629,19309957,19309981,25386029,27265457,28398641,

%U 29697029,31298269,31355297,36792901,47318969,47487889,55449689

%N Sequence of primes 2*p(k) + 3 such that 2*p(k) + 3, 2*p(k+1) + 3, 2*p(k+2) + 3, 2*p(k+3) + 3 are consecutive primes, where p(i) denotes the i-th prime.

%F a(n) = 2*A089007(n) + 3 = 2*A000040(A089009(n)) + 3 = A000040(A089524(n)).

%e p(62178)=776117, 2*776117 + 3 = 1552237 = p(117814);

%e p(62179)=776119, 2*776119 + 3 = 1552241 = p(117815);

%e p(62180)=776137, 2*776137 + 3 = 1552277 = p(117816);

%e p(62181)=776143, 2*776143 + 3 = 1552289 = p(117817).

%o (PARI) a089492(limit)={my(pv=[2,3,5,0],v3=[3,3,3,3],ks(k)=2*k+3);forprime(p=7,limit,pv[4]=p;if(vecsum(isprime(2*pv+v3))==4&&primepi(ks(pv[4]))-primepi(ks(pv[1]))==3,print1(ks(pv[1]),", "));pv[1]=pv[2];pv[2]=pv[3];pv[3]=pv[4])};

%o a089492(30000000) \\ _Hugo Pfoertner_, Aug 06 2021

%Y Subsequence of A089450.

%Y Cf. A089007, A089009, A089524.

%K nonn

%O 1,1

%A _Ray Chandler_, Nov 04 2003

%E Offset changed to 1 by _Jinyuan Wang_, Aug 06 2021