A228775 a(n) is the maximal k>=1 such that nextprime(j*n)<=(j+1)*n, j=1,...,k.

2, 3, 7, 5, 17, 14, 16, 24, 12, 19, 28, 43, 86, 80, 34, 82, 78, 73, 69, 66, 117, 329, 57, 222, 171, 228, 178, 470, 291, 359, 505, 366, 585, 576, 644, 544, 423, 742, 502, 636, 765, 466, 936, 578, 697, 682, 541, 1442, 640, 627, 615, 603, 2025, 1660, 570, 1833

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Formula

Conjectural inequality: for n>=2, a(n) <= log^2(n*a(n)). This essentially corresponds to Cramer's conjecture for prime gaps.

Example

If n=3, then, for j=1, nextprime(3)<=6; for j=2, nextprime(6)<=9; for j=3,nextprime(9)<=12; for j=4, nextprime(12)<=15; for j=5, nextprime(15)<=18; for j=6,nextprime(18)<=21; for j=7, nextprime(21)<=24, BUT for j=8, nextprime(24)>27. Thus a(3)=7.

Mathematica

a[n_] := For[k = 1, True, k++, If[NextPrime[k*n] <= (k+1)*n && NextPrime[(k+1)*n] > (k+2)*n, Return[k]]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Sep 05 2013 *)

Crossrefs

Cf. A002386, A005250, A111870.

Sequence in context: A067363 A083188 A370094 * A129543 A137440 A294639

Adjacent sequences: A228772 A228773 A228774 * A228776 A228777 A228778

Keyword

nonn

Author

Vladimir Shevelev, Sep 04 2013

Extensions

More terms from Peter J. C. Moses

Status

approved