A088281
a(1) = 11; for n > 1, palindromic primes in which a single digit is sandwiched between strings of '1's.
Original entry on oeis.org
11, 101, 131, 151, 181, 191, 11311, 11411, 1114111, 1117111, 111181111, 111191111, 1111118111111, 111111151111111, 111111181111111, 111111111161111111111, 11111111111111611111111111111, 111111111111111111131111111111111111111, 11111111111111111111111111911111111111111111111111111
Offset: 0
Cf.
A105992 (near-repunit primes),
A065074 (which contain the digit 0),
A034093 (number of primes by changing one 1 to 0),
A065083 (least k for which that = n).
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Join[{11},Select[Flatten[Table[FromDigits[Join[PadRight[{},n,1],{d},PadRight[{},n,1]]],{n,26},{d,Cases[Range[0,9],Except[1]]}]],PrimeQ]] (* Harvey P. Dale, Nov 04 2024 *)
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print1(11); for(L=1,19,for(d=0,9,d!=1 && ispseudoprime(p=10^(2*L+1)\9+(d-1)*10^L) && print1(","p))) \\ M. F. Hasler, Feb 07 2020
A088283
Palindromic primes in which a single digit is sandwiched between strings of 7's.
Original entry on oeis.org
727, 757, 787, 797, 77377, 77477, 77977, 7772777, 7774777, 7778777, 777767777, 77777677777, 7777774777777, 777777727777777, 777777757777777, 77777777677777777, 77777777977777777, 777777777727777777777
Offset: 1
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Select[Flatten[Table[FromDigits[Flatten[Join[{PadRight[{},n,7], i, PadRight[ {},n,7]}]]],{n,10},{i,0,9}]],PrimeQ] (* Harvey P. Dale, Jun 15 2015 *)
A088284
Palindromic primes in which a single digit is sandwiched between nonempty strings of 9's.
Original entry on oeis.org
919, 929, 99999199999, 99999999299999999, 9999999992999999999, 999999999999919999999999999, 99999999999999499999999999999, 999999999999999999999949999999999999999999999, 99999999999999999999999999899999999999999999999999999
Offset: 1
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Select[Flatten[Table[FromDigits[Join[PadRight[{},n,9],{d},PadRight[{},n,9]]],{n,30},{d,Range[8]}]],PrimeQ] (* Harvey P. Dale, Mar 17 2023 *)
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