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 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)]. 2
 5, 11, 13, 101, 37, 1277, 1279, 1616603, 57405419, 51448351, 76623356077, 115438255651991, 433241801791933 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS EXAMPLE 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. 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 *) PROG (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 CROSSREFS See A073615 for a very similar sequence. Sequence in context: A034924 A018607 A032481 * A073615 A275118 A275640 Adjacent sequences:  A236408 A236409 A236410 * A236412 A236413 A236414 KEYWORD nonn,more AUTHOR Don Reble, Feb 05 2014 EXTENSIONS Edited by N. J. A. Sloane, Feb 05 2014 STATUS approved

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Last modified June 22 20:00 EDT 2021. Contains 345388 sequences. (Running on oeis4.)