cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A140791 First occurrence of prime gap 10*n.

Original entry on oeis.org

139, 887, 4297, 19333, 31907, 43331, 173359, 542603, 404851, 396733, 1468277, 1895359, 5518687, 7621259, 13626257, 33803689, 27915737, 17051707, 142414669, 378043979, 20831323, 47326693, 607010093, 391995431, 387096133, 944192807
Offset: 1

Views

Author

Lekraj Beedassy, Jul 14 2008

Keywords

References

  • J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 139, pp 47, Ellipses, Paris 2008.

Crossrefs

Formula

a(n)=A000230(5n), a(3n) = A224522(n) = A058193(5n). - M. F. Hasler, Apr 09 2013

Extensions

Offset corrected by Arkadiusz Wesolowski, Jun 07 2011

A058193 Smallest prime p such that there is a gap of 6n between p and the next prime.

Original entry on oeis.org

23, 199, 523, 1669, 4297, 9551, 16141, 28229, 35617, 43331, 162143, 31397, 188029, 461717, 404851, 360653, 1444309, 2238823, 492113, 1895359, 1671781, 1357201, 3826019, 11981443, 13626257, 17983717, 39175217, 37305713, 52721113
Offset: 1

Views

Author

Labos Elemer, Nov 28 2000

Keywords

Examples

			d = 72 appears after 31397, while smaller d = 54, 60, 66 come later, following primes 35617, 43331, 162143, respectively.
		

Crossrefs

Programs

  • Mathematica
    Module[{nn=32*10^5,prs,gps},prs=Prime[Range[nn]];gps=Differences[prs];Table[SelectFirst[Thread[{Most[prs],gps}],#[[2]]==6n&],{n,30}]][[;;,1]] (* Harvey P. Dale, Mar 03 2025 *)
  • PARI
    a(n) = {p=3; q = nextprime(p+1); while((q-p) != 6*n, p = q; q = nextprime(q+1)); p;} \\ Michel Marcus, Mar 12 2016

Formula

a(n) = A000230(3n).

Extensions

Offset corrected by M. F. Hasler, Apr 09 2013

A101232 First occurrence of prime gap 10^n.

Original entry on oeis.org

2, 139, 396733, 22439962446379651
Offset: 0

Views

Author

Lekraj Beedassy, Dec 16 2004

Keywords

Crossrefs

A062530 Smallest prime p such that there is a gap of 2^n between p and previous prime.

Original entry on oeis.org

3, 5, 11, 97, 1847, 5623, 89753, 3851587, 1872852203, 1999066711903, 22790428875365903, 5333419265419188034369535864127397, 55128448018333565337014555712123010955456071077000028555991473847
Offset: 0

Views

Author

Labos Elemer, Jun 25 2001

Keywords

Comments

The next two terms are <= 13615411331526592827872074749865096844383295034548454421 and 768784577114627305753353689789300110953010089817032096740065409732504678169114467301254783622575120297131239844 respectively. - Larry Reeves (larryr(AT)acm.org), Jun 13 2002

Examples

			a(2) = 11 because 7 and 11 are consecutive primes with difference 4. - _Sascha Kurz_, Mar 05 2002
		

Crossrefs

Programs

  • PARI
    a(n) = {q = 2; p = nextprime(q+1); gap = 2^n; while(p - q != gap, q = p; p = nextprime(p+1)); p;} \\ Michel Marcus, Dec 26 2013

Formula

a(n) = A000230(2^(n-1)) + 2^n = Min{p | p-prevprime(p) = 2^n}. - Amarnath Murthy, Feb 24 2002
a(n) = A151800(A062529(n)). - Amiram Eldar, Nov 04 2024

Extensions

More terms from Sascha Kurz, Mar 05 2002
Further terms from Larry Reeves (larryr(AT)acm.org), Jun 13 2002
Edited by N. J. A. Sloane Aug 31 2009 at the suggestion of R. J. Mathar
a(11)-a(12) calculated from the data at A062529 by Amiram Eldar, Nov 04 2024

A204813 Primes followed by a gap of 256 = nextprime(p)-p.

Original entry on oeis.org

1872851947, 2362150363, 2394261637, 2880755131, 2891509333, 3353981623, 3512569873, 3727051753, 3847458487, 4008610423, 4486630573, 4541745583, 4755895531, 4837532347, 5227869607, 5389475977, 6201260587, 6229685347, 6952228483, 7325665111, 7414468513
Offset: 1

Views

Author

M. F. Hasler, Jan 19 2012

Keywords

Crossrefs

Programs

  • PARI
    list_gaps(g=256,f,N=25,p=0)=for(c=1,N,while(g+p!=p=nextprime(p+1),);if(f,write(f".txt",c" ",p-g),print1(", "p-g)))

Extensions

a(8)-a(21) from Washington Bomfim

A062531 Index of smallest prime p such that there is a gap of 2^n between p and next prime.

Original entry on oeis.org

2, 4, 24, 282, 738, 8688, 273413, 92276646, 73268943890, 622074604151528
Offset: 1

Views

Author

Labos Elemer, Jun 25 2001

Keywords

Crossrefs

Formula

a(n) =A000720[A000230[2^(n-1)]] = Pi[Min{p|p-prevprime(p)=2^n}]

Extensions

a(9)-a(10) from Daniel Suteu, Nov 18 2018 [based on data from A062529]
Showing 1-6 of 6 results.