A077787 Numbers k such that (10^k - 1)/9 + 5*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

21, 29, 81, 119, 321, 825, 1121, 2579, 3693

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.

a(10) > 4*10^5. - _Robert Price, Jan 23 2025

Examples

			21 is a term because (10^21 - 1)/9 + 5*10^10 = 111111111161111111111.
		

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...11611...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^n + 45*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 4000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A107126(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018