OFFSET
1,3
COMMENTS
A number n is in the sequence iff the palindromic number 1(n).3.1(n) is prime (1(n) means n copies of 1; dot between numbers means concatenation). If n is a positive term of the sequence then n is not of the form 3m, 6m+4, 12m+10, 28m+5, 28m+8, etc. (the proof is easy).
The palindromic number 1(n).2.1(n) is never prime for n > 0 because it is (1.0(n-1).1)*(1(n+1)). - Robert Israel, Jun 11 2015
a(7) > 10^5. - Robert Price, Apr 02 2016
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 11...11311...11
FORMULA
a(n) = (A077779(n-1)-1)/2, for n > 1. [Corrected by M. F. Hasler, Feb 06 2020]
EXAMPLE
19 is in the sequence because the palindromic number (10^(2*19+1)+18*10^19-1)/9 = 1(19).3.1(19) = 111111111111111111131111111111111111111 is prime.
MAPLE
select(n -> isprime((10^(2*n+1)+18*10^n-1)/9), [$0..100]); # Robert Israel, Jun 11 2015
MATHEMATICA
Do[If[PrimeQ[(10^(2n + 1) + 18*10^n - 1)/9], Print[n]], {n, 2500}]
PROG
(PARI) for(n=0, 1e4, if(ispseudoprime(t=(10^(2*n+1)+18*10^n)\9), print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Farideh Firoozbakht, May 19 2005
EXTENSIONS
Edited by Ray Chandler, Dec 28 2010
STATUS
approved