A068651
Primes in which a string of 2's is sandwiched between two 9's.
Original entry on oeis.org
929, 9222229, 9222222222229
Offset: 1
A056251
Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) - 17 for n > 0.
Original entry on oeis.org
1, 11, 13, 29, 103, 125, 341, 599, 9823
Offset: 1
313 is prime, hence 1 is a term.
- Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
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Flatten[Position[NestList[10#-17&,33,600],?PrimeQ]-1] (* This generates the first 8 terms of the sequence. Changing the last constant from 600 to 9825 will generate all 9 terms of the sequence but it will take a long time to do so. - _Harvey P. Dale, May 16 2012 *)
Select[Range[0, 2000], PrimeQ[(280 10^# + 17) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)
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a=33;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-17)
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for(n=0,1500,if(isprime((280*10^n+17)/9),print1(n,",")))
Additional comments from
Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
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]
A082704
Numbers k such that (28*10^(k-1) + 17)/9 is a depression prime.
Original entry on oeis.org
3, 13, 15, 31, 105, 127, 343, 601, 9825
Offset: 1
k=15 -> (28*10^(15-1) + 17)/9 = 311111111111113.
- C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.
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