OFFSET
1,2
COMMENTS
n is in the sequence iff the palindromic number 1(n).7.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+1, 6m, 6m+2, 7m+2, 16m+9, 16m+14, 18m+1, 18m+7, 22m+13, 22m+19, etc. (the proof is easy).
a(9) > 10^5. - Robert Price, Apr 30 2017
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...11711...11
FORMULA
a(n) = (A077789(n)-1)/2.
EXAMPLE
3 is in the sequence because (10^(2*3+1)+54*10^3-1)/9=1(3).7.1(3)=1117111 is prime.
2933 is in the sequence because (10^(2*2933+1)+54*10^2933-1)/9=1(2933).7.1(2933) is prime.
MATHEMATICA
Do[If[PrimeQ[(10^(2n + 1) + 54*10^n - 1)/9], Print[n]], {n, 3250}]
PROG
(PARI) for(n=0, 1e4, if(ispseudoprime(t=(10^(2*n+1)+54*10^n)\9), print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011
CROSSREFS
KEYWORD
nonn,more,base
AUTHOR
Farideh Firoozbakht, May 19 2005
EXTENSIONS
Edited by Ray Chandler, Dec 28 2010
a(6)-a(8) from Robert Price, Apr 30 2017
STATUS
approved