

A107648


Numbers n such that (10^(2n+1)+63*10^n1)/9 is prime.


44




OFFSET

1,2


COMMENTS

n is in the sequence iff the palindromic number 1(n).8.1(n) is prime (dot between numbers means concatenation). Let f(n)=(10^(2n+1)+63*10^n1)/9 then for all nonnegative integers m we have: I. 3 divides f(3m+2) II. 19 divides f(18m+13) III. 29 divides f(28*m+16) & 29 divides f(28*m+25) IV. 31 divides f(30*m+2) & 31 divides f(30*m+17) V. 41 divides f(5m+3), etc. So if n is in the sequence then n is not of the forms 3m+2, 18m+13, 28m+16 28m+25, 30m+2, 30m+17, 5m+3, etc.
a(9) > 10^5.  Robert Price, Oct 30 2017


REFERENCES

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 199697, pp. 19.
Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery, An Introduction to the Theory Of Numbers, Fifth Edition, John Wiley and Sons, Inc., NY 1991, p. 141.


LINKS

Table of n, a(n) for n=1..8.
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 11...11811...11
Index entries for primes involving repunits.


FORMULA

a(n) = (A077791(n)1)/2.


EXAMPLE

7 is in the sequence because (10^15+63*10^71)/9=1(7).8.1(7)=111111181111111 is prime.
666 is in the sequence because (10^(2*666+1)+63*10^6661)/9=1(666).8.1(666) is prime.


MATHEMATICA

Do[If[PrimeQ[(10^(2n + 1) + 63*10^n  1)/9], Print[n]], {n, 4000}]


PROG

(PARI) for(n=0, 1e4, if(ispseudoprime(t=(10^(2*n+1)+63*10^n)\9), print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011


CROSSREFS

Cf. A004023, A077775A077798, A107123A107127, A107648, A107649, A115073, A183174A183187.
Sequence in context: A102133 A192121 A012760 * A004786 A263357 A195387
Adjacent sequences: A107645 A107646 A107647 * A107649 A107650 A107651


KEYWORD

nonn,more,base


AUTHOR

Farideh Firoozbakht, May 19 2005


EXTENSIONS

Edited by Ray Chandler, Dec 28 2010


STATUS

approved



