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A107648 Numbers n such that (10^(2n+1)+63*10^n-1)/9 is prime. 45
1, 4, 6, 7, 384, 666, 675, 3165 (list; graph; refs; listen; history; text; internal format)
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^n-1)/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, 1996-97, pp. 1-9.
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
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
FORMULA
a(n) = (A077791(n)-1)/2.
EXAMPLE
7 is in the sequence because (10^15+63*10^7-1)/9=1(7).8.1(7)=111111181111111 is prime.
666 is in the sequence because (10^(2*666+1)+63*10^666-1)/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
Sequence in context: A192121 A012760 A333742 * A004786 A263357 A195387
KEYWORD
nonn,more,base
AUTHOR
Farideh Firoozbakht, May 19 2005
EXTENSIONS
Edited by Ray Chandler, Dec 28 2010
STATUS
approved

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Last modified March 3 21:06 EST 2024. Contains 370517 sequences. (Running on oeis4.)