login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A228775 a(n) is the maximal k>=1 such that nextprime(j*n)<=(j+1)*n, j=1,...,k. 0
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 (list; graph; refs; listen; history; text; internal format)
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: A124440 A067363 A083188 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 26 14:22 EST 2022. Contains 358362 sequences. (Running on oeis4.)