A107127 Numbers n such that (10^(2n+1)+54*10^n-1)/9 is prime.

0, 3, 33, 311, 2933, 22235, 39165, 41585

Offset: 1

Author

Farideh Firoozbakht, May 19 2005

Keywords

• nonn
• more
• base

Comments

n is in the sequence iff the palindromic number 1(n).7.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+1, 6m, 6m+2, 7m+2, 16m+9, 16m+14, 18m+1, 18m+7, 22m+13, 22m+19, etc. (the proof is easy).

a(9) > 10^5. - Robert Price, Apr 30 2017

Examples

			3 is in the sequence because (10^(2*3+1)+54*10^3-1)/9=1(3).7.1(3)=1117111 is prime.
2933 is in the sequence because (10^(2*2933+1)+54*10^2933-1)/9=1(2933).7.1(2933) 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...11711...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) + 54*10^n - 1)/9], Print[n]], {n, 3250}]

PARI

for(n=0,1e4,if(ispseudoprime(t=(10^(2*n+1)+54*10^n)\9),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = (A077789(n)-1)/2.

Extensions

Edited by Ray Chandler, Dec 28 2010

a(6)-a(8) from Robert Price, Apr 30 2017