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 1-10 of 17 results. Next

A096497 Prime following n-th repunit.

Original entry on oeis.org

2, 13, 113, 1117, 11113, 111119, 1111151, 11111117, 111111113, 1111111121, 11111111113, 111111111149, 1111111111139, 11111111111123, 111111111111229, 1111111111111123, 11111111111111119, 111111111111111131, 1111111111111111171, 11111111111111111131, 111111111111111111157, 1111111111111111111189
Offset: 1

Views

Author

Labos Elemer, Jul 09 2004

Keywords

Comments

Not equal to A068693: first and 2nd terms differ.

Links

Crossrefs

Cf. A068693, A002275.

Programs

  • Mathematica
    Table[NextPrime[(10^n-1)/9], {n, 40}]
Table[NextPrime[FromDigits[PadRight[{},n,1]]],{n,30}] (* Harvey P. Dale, Aug 11 2023 *)
  • PARI
    a(n) = nextprime((10^n-1)/9 + 1); \\ Michel Marcus, May 02 2016
  • Python
    from sympy import nextprime
def A096497(n):
    return nextprime((10**n-1)//9) # Chai Wah Wu, Nov 04 2019

Formula

a(n) = A002275(n) + A096869(n) = A096498(n) + A096499(n).

A099656 a(n) is the least prime following A002276(n) repdigits.

Original entry on oeis.org

2, 3, 23, 223, 2237, 22229, 222247, 2222239, 22222223, 222222227, 2222222243, 22222222223, 222222222301, 2222222222243, 22222222222229, 222222222222227, 2222222222222281, 22222222222222301, 222222222222222281
Offset: 0

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Examples

			n=2: 22 is followed by 23.

Links

Crossrefs

Cf. A003618, A003617, A096497, A096498, A068104, A002275-A002283.

Programs

  • Maple
    seq(nextprime(2*(10^i-1)/9), i=0..20); # Robert Israel, Aug 25 2017
  • Mathematica
    Table[NextPrime[2*(10^n-1)/9], {n, 0, 35}]
Table[ NextPrime[2*(10^n - 1)/9], {n, 0, 18}] (* Robert G. Wilson v, Nov 20 2004 *)
Table[NextPrime[FromDigits[PadRight[{},n,2]]],{n,0,20}] (* Harvey P. Dale, Dec 15 2021 *)

A099668 a(n) is the largest prime before A002282(n) repdigits.

Original entry on oeis.org

7, 83, 887, 8887, 88883, 888887, 8888861, 88888883, 888888887, 8888888837, 88888888859, 888888888887, 8888888888857, 88888888888873, 888888888888883, 8888888888888753, 88888888888888801, 888888888888888859, 8888888888888888881, 88888888888888888879, 888888888888888888857
Offset: 1

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Examples

			n=2: 83 is before 88.

Crossrefs

Cf. A002282, A003618, A003617, A007917, A096497, A096498, A068104, A002275-A002283, A099656-A099667.

Programs

  • Mathematica
    Table[NextPrime[8*(10^n-1)/9, -1], {n, 1, 35}]
Table[NextPrime[FromDigits[PadRight[{},n,8]],-1],{n,20}] (* Harvey P. Dale, Jul 12 2014 *)

Formula

a(n) = A007917(A002282(n)). - Amiram Eldar, Jun 29 2025

A096499 Difference between prime following and prime preceding n-th repunit.

Original entry on oeis.org

6, 4, 8, 20, 10, 60, 16, 4, 24, 54, 46, 46, 70, 176, 84, 12, 40, 134, 104, 104, 92, 24, 84, 270, 300, 130, 414, 90, 88, 240, 148, 198, 12, 64, 12, 300, 66, 70, 80, 102, 420, 142, 630, 140, 600, 88, 176, 312, 80, 96, 460, 132, 420, 284, 144, 408, 312, 180, 44, 300
Offset: 2

Views

Author

Labos Elemer, Jul 09 2004

Keywords

Examples

			n=2: 2nd repunit=11, 13-7=6=a[2].

Crossrefs

Cf. A068693, A002275, A096497, A096498.

Programs

  • Mathematica
    <Harvey P. Dale, Sep 06 2015 *)

Formula

a(n) = A096497(n) - A096498(n) = A096869(n) + A096870(n).

A096870 Difference between the n-th repunit and the previous prime.

Original entry on oeis.org

4, 2, 2, 18, 2, 20, 10, 2, 14, 52, 8, 18, 58, 58, 72, 4, 20, 74, 84, 58, 14, 18, 82, 168, 28, 50, 168, 84, 8, 138, 112, 82, 2, 28, 2, 62, 34, 50, 74, 24, 8, 54, 204, 22, 428, 40, 118, 200, 72, 40, 30, 42, 284, 44, 114, 268, 80, 18, 4, 74, 142, 182, 140, 112, 214, 152, 90
Offset: 2

Views

Author

Robert G. Wilson v, Jul 12 2004

Keywords

Links

Crossrefs

Cf. A096869.

Programs

  • Maple
    f:= proc(n) local r; r:= (10^n-1)/9; r - prevprime(r) end proc:
map(f, [$2..100]); # Robert Israel, Feb 23 2017
  • Mathematica
    PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; Table[(10^n - 1)/9 - PrevPrim[(10^n - 1)/9], {n, 2, 70}]
Table[With[{ru=(10^n-1)/9},ru-NextPrime[ru,-1]],{n,2,70}] (* Harvey P. Dale, Aug 14 2011 *)

Formula

a(n) = A002275(n) - A096498(n) = A096499(n) - A096869(n).

A099667 a(n) is the largest prime before A002281(n); repdigits repeating 7.

Original entry on oeis.org

5, 73, 773, 7759, 77773, 777769, 7777769, 77777761, 777777773, 7777777741, 77777777767, 777777777773, 7777777777771, 77777777777753, 777777777777773, 7777777777777753, 77777777777777747, 777777777777777743
Offset: 1

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Examples

			n=2: 73 is before 77.

Links

Crossrefs

Cf. A003618, A003617, A096497, A096498, A068104, A002275-A002283, A099656-A099668.

Programs

  • Mathematica
    Table[NextPrime[7 (10^n - 1)/9, -1], {n, 35}]
(* Second program: *)
Rest[NextPrime[#,-1]&/@LinearRecurrence[{11,-10},{0,7},25]] (* Harvey P. Dale, May 24 2015 *)

Extensions

Name changed by David A. Corneth, Sep 01 2017

A099658 a(n) is the smallest prime greater than 4(10^n - 1)/9.

Original entry on oeis.org

2, 5, 47, 449, 4447, 44449, 444449, 4444469, 44444453, 444444457, 4444444447, 44444444497, 444444444461, 4444444444493, 44444444444459, 444444444444461, 4444444444444463, 44444444444444461, 444444444444444469, 4444444444444444537, 44444444444444444447
Offset: 0

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Comments

a(n) = smallest prime > A002278(n).

Examples

			n=4: 44 is followed by 47.

Crossrefs

Cf. A003618, A003617, A096497, A096498, A068104, A002275-A002283, A099656-A099668.

Programs

  • Mathematica
    Table[NextPrime[4*(10^n-1)/9], {n, 0, 35}]

Extensions

Checked by N. J. A. Sloane, Jan 27 2007
Mathematica program edited by Harvey P. Dale, Jul 16 2024

A099659 a(n) is the least prime following A002279(n) repdigits.

Original entry on oeis.org

7, 59, 557, 5557, 55579, 555557, 5555567, 55555559, 555555587, 5555555557, 55555555619, 555555555559, 5555555555593, 55555555555573, 555555555555557, 5555555555555573, 55555555555555639, 555555555555555559, 5555555555555555621, 55555555555555555567, 555555555555555555619
Offset: 1

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Examples

			n=2: 55 is followed by 59.

Crossrefs

Cf. A003618, A003617, A096497, A096498, A068104, A002275-A002283, A099656-A099668.

Programs

  • Mathematica
    Table[NextPrime[5*(10^n-1)/9], {n, 1, 35}]

Extensions

Offset corrected by Georg Fischer, Mar 12 2024

A099660 a(n) is the least prime following A002280[n] repdigits.

Original entry on oeis.org

2, 7, 67, 673, 6673, 66683, 666667, 6666679, 66666667, 666666667, 6666666757, 66666666667, 666666666671, 6666666666683, 66666666666737, 666666666666719, 6666666666666719, 66666666666666713, 666666666666666773
Offset: 0

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Examples

			n=6: 66 is followed by 67.

Crossrefs

Cf. A003618, A003617, A096497, A096498, A068104, A002275-A002283, A099656-A099668.

Programs

  • Mathematica
    Table[NextPrime[6*(10^n-1)/9], {n, 0, 35}]
NextPrime/@Table[FromDigits[PadRight[{},n,6]],{n,0,20}] (* Harvey P. Dale, Feb 25 2015 *)

Extensions

First Mathematica program corrected by Harvey P. Dale, Feb 25 2015

A099662 a(n) is the least prime following A002282(n) repdigits.

Original entry on oeis.org

2, 11, 89, 907, 8893, 88897, 888917, 8888927, 88888901, 888888901, 8888888891, 88888888901, 888888888919, 8888888888921, 88888888888889, 888888888888907, 8888888888888927, 88888888888888889, 888888888888888947
Offset: 0

Views

Author

Labos Elemer, Nov 17 2004

Keywords

Examples

			n=8: 88 is followed by 89.

Crossrefs

Cf. A003618, A003617, A096497, A096498, A068104, A002275-A002283, A099656-A099668.

Programs

  • Mathematica
    Table[NextPrime[8*(10^n-1)/9], {n, 0, 35}]
Showing 1-10 of 17 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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