A077788 Numbers k such that 7*(10^k - 1)/9 - 10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

9, 11, 17, 23, 2489, 3371, 4019, 29315, 30237, 40665, 101661, 150125

Offset: 1

Author

Patrick De Geest, Nov 16 2002

Keywords

• more
• nonn
• base

Comments

Prime versus probable prime status and proofs are given in the author's table.

Examples

			11 is a term because 7*(10^11 - 1)/9 - 10^5 = 77777677777.
		

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...77677...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^n - 9*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 30300, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183181(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018

a(10) from Robert Price, Oct 07 2023

a(11) from Robert Price, Oct 17 2023

a(12) from Robert Price, Dec 06 2023