OFFSET
1,1
COMMENTS
Prime versus probable prime status and proofs are given in the author's table.
a(23) > 2*10^5. - Robert Price, Jan 29 2016
Primes of the form (10^k-1)/3 - 2*10^floor(k/2) are obtained for k in (2, 3, 6, 7, 8, 10, 15, 22, 34, 123, 126, 144, 181, 185, 198, 534, 539, 597, 606, ...). For example (10^2 - 1)/3 - 2*10^1 = 13 is also prime. However, for even k the result is not palindromic. See A077775-A077798, A107123-A107127 for PWP's with digits other than 3 and 1. - M. F. Hasler, Mar 03 2019
REFERENCES
C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.
LINKS
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 33...33133...33
FORMULA
a(n) = 2*A183174(n) + 1.
EXAMPLE
a(3) = 15 corresponds to the prime (10^15 - 1)/3 - 2*10^7 = 333333313333333.
MATHEMATICA
Do[ If[ PrimeQ[(10^n - 6*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 49100, 2}] (* Robert G. Wilson v, Dec 16 2005 *)
PROG
(PARI) is(n)=bittest(n, 0)&&ispseudoprime(10^n\3-2*10^(n\2)) \\ M. F. Hasler, Mar 03 2019
CROSSREFS
KEYWORD
more,nonn,base
AUTHOR
Patrick De Geest, Nov 16 2002
EXTENSIONS
a(21)-a(22) from Robert Price, Jan 29 2016
a(21) corrected by Robert Price, Feb 03 2016
Name corrected by Jon E. Schoenfield, Oct 31 2018
Name edited by M. F. Hasler, Mar 03 2019
STATUS
approved