OFFSET
1,1
COMMENTS
n is in the sequence iff the palindromic number 1(n).6.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m + 1, 16m + 2, 16m + 5, 22m + 1, 22m + 9, etc. (the proof is easy).
a(10) > 10^5. - Robert Price, Sep 28 2015
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...11611...11
FORMULA
a(n) = (A077787(n)-1)/2.
EXAMPLE
14 is in the sequence because (10^(2*14+1)+45*10^14-1)/9=1(14).6.1(14) = 11111111111111611111111111111 is prime.
MATHEMATICA
Do[If[PrimeQ[(10^(2n + 1) + 45*10^n - 1)/9], Print[n]], {n, 2500}]
Position[Table[FromDigits[Join[PadRight[{}, n, 1], {6}, PadRight[{}, n, 1]]], {n, 1850}], _?PrimeQ]//Flatten (* Harvey P. Dale, Jun 22 2017 *)
PROG
(PARI) is(n)=ispseudoprime((10^(2*n+1)+45*10^n-1)/9) \\ Charles R Greathouse IV, Jun 06 2017
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Farideh Firoozbakht, May 19 2005
EXTENSIONS
Edited by Ray Chandler, Dec 28 2010
STATUS
approved