A183180 Numbers k such that (7*10^(2k+1) - 18*10^k - 7)/9 is prime.

0, 1, 7, 13, 58, 129, 253, 1657, 2244, 2437, 7924, 9903, 11899, 18157, 18957, 23665, 105609

Offset: 1

Author

Ray Chandler, Dec 28 2010

Keywords

• nonn
• base

Comments

a(17) > 10^5. - Robert Price, Jun 23 2017

0 could be considered part of this sequence since the formula evaluates to 5 which is a degenerate form of the near-repdigit palindrome 777...77577...777 with 0 occurrences of the digit 7. - Robert Price, Jun 23 2017

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 77...77577...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) - 18*10^n - 7)/9], Print[n]], {n, 3000}]

PARI

is(n)=ispseudoprime((7*10^(2*n+1)-18*10^n-7)/9) \\ Charles R Greathouse IV, Jun 13 2017

Formula

a(n) = (A077785(n) - 1)/2.

Extensions

a(16) from Robert Price, Jun 23 2017

a(17) from Robert Price, Oct 12 2023