A099656 -id:A099656 - cp's OEIS frontend

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

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

Offset: 1

Labos Elemer, Nov 17 2004

			n=2: 83 is before 88.

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

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 *)

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

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

Labos Elemer, Nov 17 2004

			n=2: 73 is before 77.

Michael De Vlieger, Table of n, a(n) for n = 1..1000

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

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 *)

Name changed by David A. Corneth, Sep 01 2017

A178000 Largest n-digit prime with the maximum number of digits equal to 2.

Original entry on oeis.org

2, 29, 229, 2221, 22229, 922223, 9222229, 22222223, 222222227, 7222222229, 22222222223, 522222222229, 9222222222229, 22222222222229, 222222222222227, 9222222222222227, 72222222222222221, 222222222222222221

Offset: 1

Lekraj Beedassy, May 17 2010

Select first for most 2's, then take the largest.
In more detail: To get a(n), look at the list of all the n-digit primes. Suppose k is the maximum number of 2's of any number on the list. Throw out any prime on the list that does not contain k 2's. Then a(n) = maximal number that is left on the list. - N. J. A. Sloane, Mar 20 2018
For n <= 1000, a(n) has at most two non-2's.  What is the first n for which it has more than two? - Robert Israel, Mar 20 2018

Robert Israel, Table of n, a(n) for n = 1..999

Cf. A037057, A099656, A177999.

# This program will return FAIL if a(n) has more than two digits <> 2.
f:= proc(n)
   local k1,d2,k2,t;
   for k1 in [9,7,3,1] do if isprime(2/9*(10^n-1)+k1-2) then return 2/9*(10^n-1)+k1-2 fi od;
   for d2 from n to 2 by -1 do
     for k2 in [9,8,7,6,5,4,3] do
       for k1 in [9,7,3,1] do
         t:= 2/9*(10^(n)-1)+(k2-2)*10^(d2-1) + k1-2;
         if isprime(t) then return t fi;
  od od od:
  FAIL
end proc:
f(1):= 2:
seq(f(n),n=1..30); # Robert Israel, Mar 20 2018

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

Labos Elemer, Nov 17 2004

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

			n=4: 44 is followed by 47.

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

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

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

Labos Elemer, Nov 17 2004

			n=2: 55 is followed by 59.

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

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

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

Labos Elemer, Nov 17 2004

			n=6: 66 is followed by 67.

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

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 *)

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

Labos Elemer, Nov 17 2004

			n=8: 88 is followed by 89.

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

Table[NextPrime[8*(10^n-1)/9], {n, 0, 35}]

A099664 a(n) is the largest prime before A002278(n).

Original entry on oeis.org

3, 43, 443, 4441, 44417, 444443, 4444409, 44444399, 444444443, 4444444429, 44444444441, 444444444443, 4444444444439, 44444444444353, 444444444444421, 4444444444444423, 44444444444444411, 444444444444444419

Offset: 1

Labos Elemer, Nov 17 2004

			n=2: 43 is before 44.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Mathematica
```
<Harvey P. Dale, Feb 25 2013 *)
```

A099657 a(n) is the least prime following A002277(n) repdigits.

Original entry on oeis.org

2, 5, 37, 337, 3343, 33343, 333337, 3333373, 33333347, 333333349, 3333333403, 33333333343, 333333333367, 3333333333347, 33333333333437, 333333333333389, 3333333333333343, 33333333333333391, 333333333333333391

Offset: 0

Labos Elemer, Nov 17 2004

			n=3: 33 is followed by 37.

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

Table[NextPrime[3*(10^n-1)/9], {n, 0, 35}]

A099661 a(n) is the least prime following A002281(n) repdigits.

Original entry on oeis.org

2, 11, 79, 787, 7789, 77783, 777781, 7777801, 77777803, 777777799, 7777777781, 77777777827, 777777777841, 7777777777859, 77777777777837, 777777777777787, 7777777777777867, 77777777777777797, 777777777777777817

Offset: 0

Labos Elemer, Nov 17 2004

			n=6: 77 is followed by 79.

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

Table[NextPrime[7*(10^n-1)/9], {n, 0, 35}]
NextPrime/@LinearRecurrence[{11,-10},{0,7},35] (* Harvey P. Dale, Dec 12 2021 *)

cp's OEIS Frontend

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

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

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A178000 Largest n-digit prime with the maximum number of digits equal to 2.

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

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

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

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

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Mathematica

A099664 a(n) is the largest prime before A002278(n).

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A099657 a(n) is the least prime following A002277(n) repdigits.

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