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A077794
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.
2
53, 757, 2493, 3597, 5835, 46069, 95019, 104281, 134809
OFFSET
1,1
COMMENTS
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
1888529 is a term but its position is not known. - Jeppe Stig Nielsen, Jan 12 2024
a(10) > 600000. - Serge Batalov, Jan 17 2024
REFERENCES
C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.
FORMULA
a(n) = 2*A183187(n) + 1.
EXAMPLE
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.
MATHEMATICA
Do[ If[ PrimeQ[10^n - 1*10^Floor[n/2] - 1], Print[n]], {n, 3, 104300, 2}] (* Robert G. Wilson v, Dec 16 2005 *)
PROG
(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
KEYWORD
more,nonn,base
AUTHOR
Patrick De Geest, Nov 16 2002
EXTENSIONS
a(9) from PWP table, added by Patrick De Geest, Nov 05 2014
STATUS
approved