

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
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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

Table of n, a(n) for n=2..69.


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



