A107126 Numbers n such that (10^(2n+1)+45*10^n-1)/9 is prime.

10, 14, 40, 59, 160, 412, 560, 1289, 1846

Offset: 1

Author

Farideh Firoozbakht, May 19 2005

Keywords

• nonn
• base

Comments

n is in the sequence iff the palindromic number 1(n).6.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m + 1, 16m + 2, 16m + 5, 22m + 1, 22m + 9, etc. (the proof is easy).

a(10) > 200000 - Robert Price, Jan 23 2025

Examples

			14 is in the sequence because (10^(2*14+1)+45*10^14-1)/9=1(14).6.1(14) = 11111111111111611111111111111 is prime.
		

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...11611...11
• Index entries for primes involving repunits.

Crossrefs

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Programs

Mathematica

Do[If[PrimeQ[(10^(2n + 1) + 45*10^n - 1)/9], Print[n]], {n, 2500}]
Position[Table[FromDigits[Join[PadRight[{},n,1],{6},PadRight[{},n,1]]],{n,1850}],?PrimeQ]//Flatten (* _Harvey P. Dale, Jun 22 2017 *)

PARI

is(n)=ispseudoprime((10^(2*n+1)+45*10^n-1)/9) \\ Charles R Greathouse IV, Jun 06 2017

Formula

a(n) = (A077787(n)-1)/2.

Extensions

Edited by Ray Chandler, Dec 28 2010.