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
Original entry on oeis.org
117814, 303839, 588398, 641658, 667591, 718808, 755409, 940389, 1168122, 1198507, 1229482, 1229483, 1588488, 1698574, 1764688, 1840175, 1933195, 1936524, 2249818, 2849725, 2859255, 3307463, 3363452, 3414415, 3481752
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).
Showing 1-3 of 3 results.