A068650
Primes in which a string of 1's is sandwiched between two 3's.
Original entry on oeis.org
313, 3111111111113, 311111111111113, 3111111111111111111111111111113, 311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
Offset: 1
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a := 3:b := 1:i := 1:for n from 0 to 500 do c := a+10*(10^n-1)/9*b+10^(n+1)*a; if(isprime(c)) then d[i] := c; i := i+1; end if; end do:q := seq(d[j],j=1..i-1);
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Select[Table[10*FromDigits[PadRight[{3},n,1]]+3,{n,2,110}],PrimeQ] (* Harvey P. Dale, Dec 18 2022 *)
A068646
Primes in which a string of 5's is sandwiched between two 1's.
Original entry on oeis.org
11, 151, 15551, 155555555555555555551, 155555555555555555555555555555551
Offset: 1
11 is also a member in which a string of 0 5's is there between two one's.
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a := 1:b := 5:i := 1:for n from 0 to 500 do c := a+10*(10^n-1)/9*b+10^(n+1)*a; if(isprime(c)) then d[i] := c; i := i+1; end if; end do:q := seq(d[j],j=1..i-1);
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Select[Table[FromDigits[Join[PadRight[{1},n,5],{1}]],{n,500}],PrimeQ] (* Harvey P. Dale, Aug 08 2012 *)
A068647
Primes in which a string of 6's is sandwiched between two 1's.
Original entry on oeis.org
11, 16661, 1666666666661, 16666666666666661, 1666666666666666661, 1666666666666666666666666666666666661, 16666666666666666666666666666666666666666666666666661
Offset: 1
11 is also a member in which a string of 0 6's is there between two one's.
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Select[Table[10*FromDigits[PadRight[{1},n,6]]+1,{n,60}],PrimeQ] (* Harvey P. Dale, Jun 18 2021 *)
A056265
Indices of primes in sequence defined by A(0) = 99, A(n) = 10*A(n-1) - 61 for n > 0.
Original entry on oeis.org
1, 5, 11, 109, 3607, 37783
Offset: 1
9222229 is prime, hence 5 is a term.
- Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
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[n: n in [0..1000] | IsPrime((830*10^n + 61) div 9)]; // Vincenzo Librandi, Nov 02 2014
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Do[If[PrimeQ[(9*10^n + 2*(10^n - 1)/9)*10 + 9], Print[n]], {n, 1, 2500}]
Select[Range[2000], PrimeQ[(830 10^# + 61) / 9] &] (* Vincenzo Librandi, Nov 02 2014 *)
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a=99;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-61) \\ Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
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for(n=0,1000,if(isprime((830*10^n + 61)/9),print1(n,","))) \\ Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
3607 from
Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
A068648
Primes in which a string of 8's is sandwiched between two 1's.
Original entry on oeis.org
11, 181, 188888881, 188888888888881, 18888888888888888888888888888888888888881, 188888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
Offset: 1
11 is also a member in which a string of 0 8's is there between two one's.
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a := 1:b := 8:i := 1:for n from 0 to 500 do c := a+10*(10^n-1)/9*b+10^(n+1)*a; if(isprime(c)) then d[i] := c; i := i+1; end if; end do:q := seq(d[j],j=1..i-1);
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Select[Table[10FromDigits[PadRight[{1},n,8]]+1,{n,100}],PrimeQ] (* Harvey P. Dale, Jul 08 2020 *)
A068649
Primes in which a string of 9's is sandwiched between two 1's.
Original entry on oeis.org
11, 191, 19991, 199999991, 19999999999999999999999999999999999999991, 199999999999999999999999999999999999999999999999999999999999999999999999999999999999991
Offset: 1
11 is also a member in which a string of 0 9's is there between two one's.
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a := 1:b := 9:i := 1:for n from 0 to 500 do c := a+10*(10^n-1)/9*b+10^(n+1)*a; if(isprime(c)) then d[i] := c; i := i+1; end if; end do:q := seq(d[j],j=1..i-1);
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Select[Table[FromDigits[Join[{1}, Table[9, {i}], {1}]], {i, 0, 200}], PrimeQ]
A082718
Numbers k such that (83*10^(k-1) + 61)/9 is a depression prime.
Original entry on oeis.org
3, 7, 13, 111, 3609, 37785
Offset: 1
k=13 -> (83*10^(13-1) + 61)/9 = 9222222222229.
- C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.
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