A236411 Let p(k) denote the k-th prime; a(n) = smallest p(m) > p(n) such that the n-2 differences between [p(n), p(n+1), ..., p(2n-2)] are the same as the n-2 differences between [p(m), p(m+1), ..., p(m+n-2)].

5, 11, 13, 101, 37, 1277, 1279, 1616603, 57405419, 51448351, 76623356077, 115438255651991, 433241801791933

Offset: 2

Author

Don Reble, Feb 05 2014

Keywords

• nonn
• more

Examples

			n=5: We take the four primes [p(5)=11, 13, 17, 19], whose successive differences are 2, 4, 2. The next time we see this sequence of differences is at [101, 103, 107, 109], so a(5) = 101.
		

Crossrefs

See A073615 for a very similar sequence.

Programs

Mathematica

(* This program generates the first ten terms of the sequence.  To generate more would require significantly greater computing resources *) dbp[n_]:=Differences[ Prime[ Range[ n,2n-2]]]; With[{prs=Prime[Range[ 3500000]]}, First/@ Flatten[ Table[Select[Partition[Drop[prs,n],n-1,1], Differences[#]==dbp[n]&,1],{n,2,11}],1]] (* Harvey P. Dale, Feb 05 2014 *)

PARI

A236411 = n->{d=vector(n-2,i,prime(n+i)-prime(n));
  forprime(p=prime(n+1),,
    for(k=1,#d, isprime(p+d[k])||next(2));
    for(k=1,#d, p+d[k]==nextprime(p+if(k>1,d[k-1])+1)||next(2));
  return(p))} \\ The second k-loop would suffice, but the first makes it 5x faster. Yields a(10), a(11) in ca. 3 sec (i7, 1.9Ghz). - M. F. Hasler, Feb 05 2014. [Erroneous ')' removed, Oct 09 2023]

Extensions

Edited by N. J. A. Sloane, Feb 05 2014