A183179 Numbers n such that 7*(10^(2n+1)-1)/9 - 3*10^n is prime.

2, 3, 6, 23, 36, 69, 561, 723, 3438, 4104, 9020, 13977, 19655, 32400

Offset: 1

Author

Ray Chandler, Dec 28 2010

Keywords

• nonn
• base

Comments

Original name: Numbers n such that (7*10^(2n+1)-27*10^n-7)/9 is prime.

a(15) > 10^5. - Robert Price, Nov 23 2015

References

• C. Caldwell and H. Dubner, The near repdigit primes A(n-k-1)B(1)A(k), especially 9(n-k-1)8(1)9(k), 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 77...77477...77
• Index entries for primes involving repunits.

Crossrefs

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

Programs

Mathematica

Do[If[PrimeQ[(7*10^(2n + 1) - 27*10^n - 7)/9], Print[n]], {n, 3000}]

PARI

for(n=1, 1e3, if(ispseudoprime((7*10^(2*n+1)-27*10^n-7)/9), print1(n, ", "))) \\ Altug Alkan, Nov 23 2015

Formula

a(n) = (A077781(n)-1)/2.

Extensions

a(14) from Robert Price, Nov 23 2015