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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 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*10^7-1)/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 Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187. Sequence in context: A192121 A012760 A333742 * 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

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