A107649 Numbers n such that (10^(2n+1)+72*10^n-1)/9 is prime.

1, 4, 26, 187, 226, 874, 13309, 34016, 42589

Offset: 1

Author

Farideh Firoozbakht, May 19 2005

Keywords

• nonn
• more
• base

Comments

n is in the sequence iff the palindromic number 1(n).9.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m+5, 22m+3, 22m+7, etc. (the proof is easy).

a(10) > 200000. - _Robert Price, Jan 30 2025

Examples

			26 is in the sequence because (10^(2*26+1)+72*10^26-1)/9=1(26).9.1(26)
= 11111111111111111111111111911111111111111111111111111 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...11911...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) + 72*10^n - 1)/9], Print[n]], {n, 3000}]
prQ[n_]:=Module[{c=PadRight[{},n,1]},PrimeQ[FromDigits[Join[c,{9},c]]]]; Select[Range[13500],prQ] (* Harvey P. Dale, Jan 19 2014 *)

PARI

for(n=0,1e4,if(ispseudoprime(t=(10^(2*n+1)+72*10^n)\9),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = (A077795(n)-1)/2.

Extensions

Edited by Ray Chandler, Dec 28 2010

a(8)-a(9) from Robert Price, Sep 28 2017