A107124 Numbers k such that (10^(2*k+1)+27*10^k-1)/9 is prime.

2, 3, 32, 45, 1544

Offset: 1

Author

Farideh Firoozbakht, May 19 2005

Keywords

• nonn
• base
• more

Comments

k is in the sequence iff the palindromic number 1(k).4.1(k) is prime (dot between numbers means concatenation). If k is in the sequence then k is not of the forms 3m+1, 16m+11, 16m+12, 18m+11, 18m+15, etc. (the proof is easy).

Examples

			32 is in the sequence because the palindromic number (10^(2*32+1)+27*10^32-1)/9 = 1(32).4.1(32) =
11111111111111111111111111111111411111111111111111111111111111111 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...11411...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) + 27*10^n - 1)/9], Print[n]], {n, 2200}]
Select[Range[1600],PrimeQ[FromDigits[Join[PadRight[{},#,1],{4},PadRight[ {},#,1]]]]&] (* Harvey P. Dale, Aug 01 2017 *)

PARI

is(n)=ispseudoprime((10^(2*n+1)+27*10^n-1)/9) \\ Charles R Greathouse IV, May 22 2017

Formula

a(n) = (A077780(n)-1)/2.

Extensions

Edited by Ray Chandler, Dec 28 2010