A249011 Smallest prime(i) such that the constellation of the n following prime gaps is the same constellation as the gaps following prime(i+n).

3, 5, 59, 839, 541, 60453409

Offset

1,1

Comments

"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.

Links

Table of n, a(n) for n=1..6.

Abhiram R Devesh, Python Code for generating this sequence

Index entries for primes, gaps between

Example

a(1)=3 as the prime gap [2] is repeated in the same order for 3->5 and 5->7.
a(2)=5 as the prime gaps [2, 4] are repeated for 5->7->11 and 11->13->17.
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.

Prog

(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)); ); }
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

Crossrefs

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

Sequence in context: A049190 A174920 A158314 * A261533 A118477 A380422

Adjacent sequences: A249008 A249009 A249010 * A249012 A249013 A249014

Keyword

nonn,more

Author

Abhiram R Devesh, Oct 18 2014

Status

approved