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A077794
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Odd integers k such that 10^k - 1 - 10^((k-1)/2) is a prime of the form 9...989...9, called a palindromic wing prime or a near-repdigit palindromic prime.
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2
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OFFSET
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1,1
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COMMENTS
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Prime versus probable prime status and proofs are given in the author's table.
The corresponding primes have a(n) digits all of which are '9's except for the middle digit which is an '8'. They are too large to be listed in a sequence on their own, cf. examples. See A077775-A077798 and A107123-A107127 for palindromic wing/near-repdigit primes with other digits. - M. F. Hasler, Mar 03 2019
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REFERENCES
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C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 53 corresponds to the 53-digit prime
p = 99999999999999999999999999899999999999999999999999999.
a(2) = 757 corresponds to p = (10^757 - 1) - 10^378 = 99...99899...99.
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MATHEMATICA
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Do[ If[ PrimeQ[10^n - 1*10^Floor[n/2] - 1], Print[n]], {n, 3, 104300, 2}] (* Robert G. Wilson v, Dec 16 2005 *)
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PROG
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(PARI) is(n)=bittest(n, 0)&&ispseudoprime(10^n-1-10^(n\2))
forstep(n=1, oo, 2, is(n)&&print1(n", ")) \\ M. F. Hasler, Mar 03 2019
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CROSSREFS
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KEYWORD
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more,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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