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 *)
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).
A102810
Numbers n such that 2*prime(n)+3, 2*prime(n+1)+3, 2*prime(n+2)+3, 2*prime(n+3)+3 and 2*prime(n+4)+3 are consecutive primes.
Original entry on oeis.org
643266, 6127598, 9017291, 10371970, 10582732, 11357913, 13177036, 14860382, 30277278, 31675266, 41311665, 49626317, 50618743, 78805352, 86522154, 93614849, 106262424, 113388731, 117041604, 118113837, 140649556, 141178396
Offset: 1
A102811
Least k such that, for j from 1 to n, 2*P(k+n-j) + 3 are consecutive primes with P(i)= i-th prime.
Original entry on oeis.org
1, 3, 44, 62178, 643266
Offset: 1
For n = 1, 2*P(1) + 3 = 2*2 + 3 = 7 is prime, so a(1)=1 as P(1)=2.
For n = 2, 2*P(3) + 3 = 2*5 + 3 = 13 is prime, 2*P(4) + 3 = 2*7 + 3 = 17 is a prime consecutive to 13, so a(2)=3 as P(3)=5.
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a(n) = {my(m=1, p=vector(n, i, prime(i)), q); while(ispseudoprime(q=(2*p[1]+3)) + sum(k=2, n, (q=nextprime(q+1))==2*p[k]+3) < n, m++; p=concat(p[2..n], nextprime(p[n]+1))); m; } \\ Jinyuan Wang, Mar 20 2020
A159922
Least index m such that the five numbers 2*prime(m+k) + 3^n, k=0 to 4, are five consecutive primes.
Original entry on oeis.org
643266, 8813528, 1644953, 440421, 2826655, 1339785, 2775232, 988180, 196973, 643136, 4122122, 3477939, 182124, 6195602, 130854, 4937610, 2725523, 6118932, 231670, 478208, 2405748, 3913626, 1033788, 2945487, 22952758, 7168835, 15528738, 2753214, 2407038, 37795639
Offset: 1
For n=15, prime(m=130854) = 1739401 starts the prime sequence 1739401, 1739411, 1739417, 1739443, 1739447 of five consecutive primes.
With 3^n = 3^15 = 14348907, the five numbers 17827709 = 2*1739401+14348907, 17827729 = 2*1739411 + 14348907, 17827741 = 2*1739417 + 14348907, 17827793 = 2*1739443 + 14348907, 17827801 = 2*1739447 + 14348907 are consecutive primes, and m = 130854 is the smallest prime index of this kind, so a(n=15) = 130854.
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a(n) = {my(m=1, p=[2, 3, 5, 7, 11], q, x=3^n); while(ispseudoprime(q=(2*p[1]+x)) + sum(k=2, 5, (q=nextprime(q+1))==2*p[k]+x) < 5, m++; p=concat(p[2..5], nextprime(p[5]+1))); m; } \\ Jinyuan Wang, Mar 20 2020
Replaced the wrong value 14348916 by 14348907 (3^15=14348907). -
Pierre CAMI, May 09 2009
Showing 1-6 of 6 results.