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 A162417 Find max {primes such that p < n^2, n = 2,3,...}, then the gap g(n) between that prime and its successor. This sequence is the sequence of differences {2n - g(n)}. 1
 2, 2, 4, 4, 6, 8, 10, 14, 16, 8, 14, 20, 24, 26, 26, 24, 22, 30, 36, 38, 36, 28, 42, 38, 48, 48, 42, 44, 40, 48, 54, 62, 58, 64, 66, 68, 68, 66, 76, 58, 66, 72, 72, 80, 76, 88, 84, 86, 74, 86, 96, 90, 100, 96, 96, 92, 106, 96, 106, 114, 110, 104, 122, 120, 124, 124, 120, 114 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The unproved conjecture that 2n - g(n) > 0 would imply Legendre's conjecture, since the next prime after max {p < n^2} will always occur before (n+1)^2. LINKS FORMULA a(n) = 2*n - A058043(n). - R. J. Mathar, Jul 13 2009 MAPLE with(numtheory): A162417:=n->2*n-(ithprime(pi(n^2)+1)-ithprime(pi(n^2))): seq(A162417(n), n=2..100); # Wesley Ivan Hurt, Aug 01 2015 MATHEMATICA Table[2i - (Prime[PrimePi[i^2]+1]-Prime[PrimePi[i^2]]), {i, 2, 1000}] f[n_] := 2 n - Prime[PrimePi[n^2] + 1] + Prime[PrimePi[n^2]]; Table[ f@n, {n, 2, 69}] (* Robert G. Wilson v, Aug 17 2009 *) PROG (MAGMA) [2*n-(NthPrime(#PrimesUpTo(n^2)+1)-NthPrime(#PrimesUpTo(n^2))): n in [2..100]]; // Vincenzo Librandi, Aug 02 2015 CROSSREFS Cf. A058043. Sequence in context: A294150 A087135 A227135 * A240012 A295261 A293627 Adjacent sequences:  A162414 A162415 A162416 * A162418 A162419 A162420 KEYWORD nonn AUTHOR Daniel Tisdale, Jul 02 2009 EXTENSIONS Edited by N. J. A. Sloane, Jul 05 2009 Offset corrected by R. J. Mathar, Jul 13 2009 a(18) and further terms from Robert G. Wilson v, Aug 17 2009 STATUS approved

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Last modified March 22 04:32 EDT 2019. Contains 321406 sequences. (Running on oeis4.)