A089009
Numbers n such that 2*p(n)+3, 2*p(n+1)+3, 2*p(n+2)+3, 2*p(n+3)+3 are consecutive primes, where p(i) denotes the i-th prime.
Original entry on oeis.org
62178, 159794, 308508, 336390, 350046, 376777, 395837, 492449, 611190, 627072, 643266, 643267, 830501, 887720, 922151, 961608, 1009939, 1011676, 1174998, 1487107, 1492042, 1725364, 1754501, 1780962, 1815913, 2048082, 2235662
Offset: 1
p(62178)=776117, 2*776117+3=1552237=p(117814).
p(62179)=776119, 2*776119+3=1552241=p(117815).
p(62180)=776137, 2*776137+3=1552277=p(117816).
p(62181)=776143, 2*776143+3=1552289=p(117817).
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cpQ[n_]:=Module[{p1=2Prime[n]+3,p2=2Prime[n+1]+3,p3=2Prime[n+2]+3,p4 = 2Prime[ n+3]+3}, PrimeQ[ p1] &&NextPrime[p1]==p2&&NextPrime[p2]==p3 && NextPrime[p3]==p4]; Select[Range[2236000],cpQ] (* Harvey P. Dale, Aug 15 2020 *)
A089492
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.
Original entry on oeis.org
1552237, 4315469, 8774137, 9629197, 10048081, 10875149, 11469389, 14498741, 18280861, 18789629, 19309957, 19309981, 25386029, 27265457, 28398641, 29697029, 31298269, 31355297, 36792901, 47318969, 47487889, 55449689
Offset: 1
p(62178)=776117, 2*776117 + 3 = 1552237 = p(117814);
p(62179)=776119, 2*776119 + 3 = 1552241 = p(117815);
p(62180)=776137, 2*776137 + 3 = 1552277 = p(117816);
p(62181)=776143, 2*776143 + 3 = 1552289 = p(117817).
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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])};
a089492(30000000) \\ Hugo Pfoertner, Aug 06 2021
A089007
Sequence of primes p(n) such that 2*p(n)+3, 2*p(n+1)+3, 2*p(n+2)+3, 2*p(n+3)+3 are four consecutive primes, where p(i) denotes the i-th prime.
Original entry on oeis.org
776117, 2157733, 4387067, 4814597, 5024039, 5437573, 5734693, 7249369, 9140429, 9394813, 9654977, 9654989, 12693013, 13632727, 14199319, 14848513, 15649133, 15677647, 18396449, 23659483, 23743943, 27724843, 28224293, 28677529
Offset: 1
776117 is in the sequence because it is the 62178th prime, followed by the primes 776119, 776137 and 776143; and 2*776117+3 = 1552237, 2*776119+3 = 1552241, 2*776137+3 = 1552277 and 2*776143+3 = 1552289 which are the 117814th, 117815th, 117816th and 117817th prime respectively.
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lst = {}; Do[ If[ PrimeQ[2Prime[n] + 3], If[ PrimeQ[2Prime[n + 1] + 3], If[ PrimeQ[2Prime[n + 2] + 3], If[ PrimeQ[2Prime[n + 3] + 3], If[ PrimePi[2Prime[n] + 3] + 3 == PrimePi[2Prime[n + 3] + 3], AppendTo[lst, Prime[n]]] ]]]], {n, 2048081}] (* Robert G. Wilson v, Jan 13 2005 *)
Showing 1-3 of 3 results.