A249011 - OEIS

%I #35 Dec 05 2017 05:46:18

%S 3,5,59,839,541,60453409

%N Smallest prime(i) such that the constellation of the n following prime gaps is the same constellation as the gaps following prime(i+n).

%C "Constellation" in the title means that not only the set of the prime gaps after the two primes is the same, but the order of the prime gaps must also be preserved.

%H Abhiram R Devesh, <a href="/A249011/a249011_2.py.txt">Python Code for generating this sequence</a>

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>

%e a(1)=3 as the prime gap [2] is repeated in the same order for 3->5 and 5->7.

%e a(2)=5 as the prime gaps [2, 4] are repeated for 5->7->11 and 11->13->17.

%e a(4)=839 as the prime gaps [14, 4, 2, 4] are repeated for the 2 consecutive sets of consecutive primes 839->853->857->859->863 and 863->877->881->883->887.

%o (PARI) findspg(n, vpg) = {for (k=1, #vpg-2*n, pga = vector(n, i, vpg[k+i-1]); pgb = vector(n, i, vpg[k+n+i-1]); if (pga==pgb, return (k)););}

%o lista(nn=6, pp=10000000) = {vp = primes(pp); vpg = vector(pp-1, i, vp[i+1] - vp[i]); for (n=1, nn, ip = findspg(n, vpg); if (ip>0, print1(prime(ip), ", ")););} \\ _Michel Marcus_, Oct 25 2014

%Y Cf. A001223 (prime gaps), A249012 (order of the prime gaps not considered).

%K nonn,more

%O 1,1

%A _Abhiram R Devesh_, Oct 18 2014