A241206 -id:A241206 - cp's OEIS frontend

A268702 Largest n digit prime having at least n-1 digits equal to 1.

7, 71, 911, 8111, 16111, 911111, 1171111, 71111111, 131111111, 1711111111, 31111111111, 311111111111, 5111111111111, 41111111111111, 111151111111111, 5111111111111111, 11111611111111111, 191111111111111111, 2111111111111111111, 11111111611111111111

Offset: 1

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Feb 11 2016

			a(3) = 911 since 111, 211, 311, ..., 811 are all composites but 911 is prime. Also of the ten primes of 3 digits which contain at least 2 ones, {101, 113, 131, 151, 181, 191, 211, 311, 811, 911}, 911 is the greatest.

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Cf. A177999, A241100, A268703 - A268707, A241206.

f[n_] := Block[{k = 0, p = {}, r = (10^n - 1)/9, s = Range@ 10 - 2}, While[k < n, AppendTo[p, Select[r + 10^k*s, PrimeQ]]; k++]; p = Max@ Flatten@ p]; Array[f, 20]

a(n) = {p = precprime(10^n-1); while (#select(x->x==1, digits(p)) != n-1, p = precprime(p-1)); p;} \\ Michel Marcus, Feb 21 2016

A268707 Smallest n-digit prime having at least n-1 digits equal to 9.

Original entry on oeis.org

2, 19, 199, 1999, 49999, 199999, 2999999, 19999999, 799999999, 9199999999, 59999999999, 959999999999, 9919999999999, 59999999999999, 499999999999999, 9299999999999999, 99919999999999999, 994999999999999999, 9991999999999999999, 29999999999999999999

Offset: 1

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Feb 11 2016

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Table of n, a(n) for n = 1..1225

Cf. A037071, A241100, A268702 - A268706, A241206, A266148.

f[n_] := Block[{k = 0, p = {}, r = (10^n - 1), s = Range@ 10 - 10}, While[k < n - 0, AppendTo[p, Select[r + 10^k*s, PrimeQ]]; k++]; p = Min@ Flatten@ p]; Array[f, 20]

a(n)=my(t=10^n-1,p); forstep(d=n-1,0,-1, forstep(k=8,1,-1, p=t-10^d*k; if(ispseudoprime(p), return(p)))); -1 \\ Charles R Greathouse IV, Mar 21 2016

A178007 Largest n-digit prime with the most digits equal to 9.

Original entry on oeis.org

7, 97, 997, 9949, 99991, 999979, 9999991, 99999989, 999999929, 9999999929, 99999999599, 999999999989, 9999999999799, 99999999999959, 999999999999989, 9999999999999199, 99999999999999997, 999999999999999989, 9999999999999999919, 99999999999999999989, 999999999999999999899, 9999999999999999999929

Offset: 1

Lekraj Beedassy, May 17 2010

First maximum the number of 9's, then choose the largest.
From Robert Israel, Dec 18 2024: (Start)
This is believed to be different from A241206, as there should be infinitely many n for which there is no n-digit prime with n-1 digits equal to 9.  No examples are known; the least such n is greater than 3400. (End)

Robert Israel, Table of n, a(n) for n = 1..996

Cf. A037071, A105975, A003618, A241206, A266148.

f:= proc(n) local i,j,a,b,x,y;
     x:= 10^n-1;
     for i from 0 to n-1 do
       for a from 1 to 9 do
         y:= x - a*10^i;
         if isprime(y) then return y fi;
     od od;
     for i from 1 to n-1 do
       for a from 1 to 9 do
         for j from 0 to i-1 do
           for b from 1 to 9 do
             y:= x - a*10^i - b*10^j;
             if isprime(y) then return y fi
    od od od od;
    FAIL
end proc:
map(f, [$1..30]); # Robert Israel, Dec 16 2024

Corrected and more terms by Robert Israel, Dec 16 2024

A268703 Smallest n-digit prime having at least n-1 digits equal to 3.

Original entry on oeis.org

2, 13, 233, 2333, 23333, 313333, 3233333, 31333333, 333233333, 3233333333, 23333333333, 333313333333, 3333333333383, 33133333333333, 323333333333333, 1333333333333333, 23333333333333333, 333333133333333333, 3333313333333333333, 33313333333333333333

Offset: 1

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Feb 11 2016

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Table of n, a(n) for n = 1..1105

Cf. A037059, A241100, A268702 - A268707, A241206, A266142.

f[n_] := Block[{k = 0, p = {}, r = (10^n - 1)/3, s = Range@ 10 - 4}, While[k < n, AppendTo[p, Select[r + 10^k*s, PrimeQ]]; k++]; p = Min@ Flatten@ p]; f[1] = 2; f[2] = 13; Array[f, 20]

A268706 Largest n-digit prime having at least n-1 digits equal to 7.

Original entry on oeis.org

7, 97, 977, 7877, 97777, 787777, 7877777, 77777747, 787777777, 8777777777, 79777777777, 777777779777, 7877777777777, 77777779777777, 778777777777777, 8777777777777777, 77797777777777777, 797777777777777777, 7777877777777777777, 97777777777777777777

Offset: 1

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Feb 11 2016

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Table of n, a(n) for n = 1..1268

Cf. A241100, A268702, A268703, A268704, A268705, A268707, A241206, A266146.

f:= proc(n)
  local r,i,j,p;
  r:= 7*(10^n-1)/9;
  for p in sort([r, seq(seq(r + i*10^j, i=[$(-7)..(-1),1,2]),j=0..n-1)],`>`) do
    if isprime(p) then return p fi
  od;
  error("no prime found")
end proc:
map(f, [$1..100]); # Robert Israel, Feb 24 2016

f[n_] := Block[{k = 0, p = {}, r = 7 (10^n - 1)/9, s = Range@ 10 - 8}, While[k < n, AppendTo[p, Select[r + 10^k*s, PrimeQ]]; k++]; p = Max@ Flatten@ p]; Array[f, 20]

A268704 Greatest n-digit prime having at least n-1 digits equal to 3.

Original entry on oeis.org

7, 83, 733, 7333, 38333, 733333, 3733333, 83333333, 373333333, 3334333333, 38333333333, 383333333333, 3433333333333, 53333333333333, 383333333333333, 3733333333333333, 43333333333333333, 353333333333333333, 3333334333333333333, 33343333333333333333

Offset: 1

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Feb 11 2016

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Cf. A178001, A241100, A268702 - A268707, A241206, A266142.

f[n_] := Block[{k = 0, p = {}, r = (10^n - 1)/3, s = Range@ 10 - 4}, While[k < n, AppendTo[p, Select[r + 10^k*s, PrimeQ]]; k++]; p = Max@ Flatten@ p]; Array[f, 20]
Table[Max[Select[FromDigits/@Flatten[Permutations/@Table[PadRight[{n},k,3],{n,{1,2,4,5,7,8}}],1],IntegerLength[#]==k&&PrimeQ[#]&]],{k,20}] (* Harvey P. Dale, Apr 11 2020 *)

A268705 Smallest n-digit prime having at least n-1 digits equal to 7.

Original entry on oeis.org

2, 17, 277, 1777, 47777, 727777, 7477777, 77767777, 577777777, 1777777777, 67777777777, 377777777777, 7177777777777, 17777777777777, 577777777777777, 2777777777777777, 77777767777777777, 377777777777777777, 2777777777777777777, 71777777777777777777

Offset: 1

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Feb 11 2016

Michel Lagneau, Michael De Vlieger and Robert G. Wilson v, Table of n, a(n) for n = 1..1125

Cf. A037067, A241100, A268702 - A268706, A268707, A241206, A266146.

f[n_] := Block[{k = 0, p = {}, r = 7(10^n - 1)/9, s = Range@ 10 - 8}, While[k < n, AppendTo[p, Select[r + 10^k*s, PrimeQ]]; k++]; p = Min@ Flatten@ p]; f[1] = 2; f[2] = 17; Array[f, 20]
Table[Min[Select[FromDigits/@Flatten[Permutations/@Table[Join[ {n},PadRight[ {},k,7]],{n,0,9}],1],IntegerLength[#]==k+1&&PrimeQ[#]&]],{k,0,20}] (* Harvey P. Dale, Jan 23 2021 *)

A385280 a(n) is the number of n-digit primes of which all digits except one are the same.

Original entry on oeis.org

4, 20, 46, 43, 40, 53, 35, 49, 40, 38, 44, 52, 35, 45, 49, 42, 38, 57, 27, 45, 38, 47, 37, 52, 33, 45, 56, 38, 36, 65, 29, 56, 48, 40, 38, 58, 37, 33, 57, 40, 37, 61, 41, 39, 37, 44, 36, 55, 47, 43, 47, 43, 35, 62, 43, 46, 29, 35, 37, 56, 39, 41, 46, 48, 39, 74, 45, 34, 34, 35, 34, 67, 39, 45, 43

Offset: 1

Robert Israel, Jun 24 2025

a(n) is the number of n-digit primes obtained by changing one digit of an n-digit repdigit.

			a(5) = 40 because there are 40 5-digit primes of which all digits but one are the same, namely 10111, 11113, 11117, 11119, 11131, 11161, 11171, 11311, 11411, 16111, 22229, 23333, 31333, 33331, 33343, 33353, 33533, 38333, 44449, 47777, 49999, 59999, 67777, 71777, 76777, 77377, 77477, 77747, 77773, 77797, 77977, 79777, 79999, 88883, 94999, 97777, 98999, 99929, 99989, 99991.

Robert Israel, Table of n, a(n) for n = 1..1000

Cf. A004022, A010785, A084673, A241206.

Essentially the same as A258915.

f:= proc(n)
     local i,j,m, m2, t;
     t:= 0;
     for i from 1 to 9 do
       for j in {$0..9} minus {i} do
          if (n-1)*i + j mod 3 = 0 then next fi;
          if j = 0 then m2:= n-2 else m2:= n-1 fi;
          if not member(i,{1,3,7,9}) then m2:= 0 fi;
          t:= t + nops(select( isprime,{seq((10^n-1)/9*i + 10^m*(j-i),m=0..m2)}))
     od od;
     t
end proc:
f(1):= 4: f(2):= 20:
map(f, [$1..100]);

from gmpy2 import is_prime, digits
def a(n):
    Rn = (10**n-1)//9
    return len(set(t for d in range(1, 10) for i in range(n if d in {1, 3, 7, 9} else 1) for c in set(range(-d, 10-d))-{0} if len(digits(t:=d*Rn+c*10**i))==n and is_prime(t)))
print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Jun 25 2025

cp's OEIS Frontend

A268702 Largest n digit prime having at least n-1 digits equal to 1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A268707 Smallest n-digit prime having at least n-1 digits equal to 9.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A178007 Largest n-digit prime with the most digits equal to 9.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Extensions

A268703 Smallest n-digit prime having at least n-1 digits equal to 3.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A268706 Largest n-digit prime having at least n-1 digits equal to 7.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

A268704 Greatest n-digit prime having at least n-1 digits equal to 3.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A268705 Smallest n-digit prime having at least n-1 digits equal to 7.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A385280 a(n) is the number of n-digit primes of which all digits except one are the same.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Python