A107123 Numbers n such that (10^(2n+1)+18*10^n-1)/9 is prime.

0, 1, 2, 19, 97, 9818

Offset

1,3

Comments

A number n is in the sequence iff the palindromic number 1(n).3.1(n) is prime (1(n) means n copies of 1; dot between numbers means concatenation). If n is a positive term of the sequence then n is not of the form 3m, 6m+4, 12m+10, 28m+5, 28m+8, etc. (the proof is easy).

The palindromic number 1(n).2.1(n) is never prime for n > 0 because it is (1.0(n-1).1)*(1(n+1)). - Robert Israel, Jun 11 2015

a(7) > 10^5. - Robert Price, Apr 02 2016

References

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Table of n, a(n) for n=1..6.

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)

Makoto Kamada, Prime numbers of the form 11...11311...11

Index entries for primes involving repunits.

Formula

a(n) = (A077779(n-1)-1)/2, for n > 1. [Corrected by M. F. Hasler, Feb 06 2020]

Example

19 is in the sequence because the palindromic number (10^(2*19+1)+18*10^19-1)/9 = 1(19).3.1(19) = 111111111111111111131111111111111111111 is prime.

Maple

select(n -> isprime((10^(2*n+1)+18*10^n-1)/9), [$0..100]); # Robert Israel, Jun 11 2015

Mathematica

Do[If[PrimeQ[(10^(2n + 1) + 18*10^n - 1)/9], Print[n]], {n, 2500}]

Prog

(PARI) for(n=0, 1e4, if(ispseudoprime(t=(10^(2*n+1)+18*10^n)\9), print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Crossrefs

Cf. A004023, A077775-A077798, A107124, A107125, A107126, A107127, A107648, A107649, A115073, A183174-A183187.

Sequence in context: A056005 A034572 A041393 * A360816 A193047 A055875

Adjacent sequences: A107120 A107121 A107122 * A107124 A107125 A107126

Keyword

nonn,base,more

Author

Farideh Firoozbakht, May 19 2005

Extensions

Edited by Ray Chandler, Dec 28 2010

Status

approved