OFFSET
1,1
COMMENTS
n is in the sequence iff the palindromic number 1(n).4.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+1, 16m+11, 16m+12, 18m+11, 18m+15, etc. (the proof is easy).
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...11411...11
FORMULA
a(n) = (A077780(n)-1)/2.
EXAMPLE
32 is in the sequence because the palindromic number (10^(2*32+1)+27*10^32-1)/9 = 1(32).4.1(32) =
11111111111111111111111111111111411111111111111111111111111111111 is prime.
MATHEMATICA
Do[If[PrimeQ[(10^(2n + 1) + 27*10^n - 1)/9], Print[n]], {n, 2200}]
Select[Range[1600], PrimeQ[FromDigits[Join[PadRight[{}, #, 1], {4}, PadRight[ {}, #, 1]]]]&] (* Harvey P. Dale, Aug 01 2017 *)
PROG
(PARI) is(n)=ispseudoprime((10^(2*n+1)+27*10^n-1)/9) \\ Charles R Greathouse IV, May 22 2017
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Farideh Firoozbakht, May 19 2005
EXTENSIONS
Edited by Ray Chandler, Dec 28 2010
STATUS
approved