A077779 Numbers k such that (10^k - 1)/9 + 2*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

3, 5, 39, 195, 19637

Offset: 1

Author

Patrick De Geest, Nov 16 2002

Keywords

• nonn
• base
• more

Comments

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

a(6) > 2*10^5. - Robert Price, Apr 02 2016

The number k = 1 would also correspond to a prime, 3, but not "near-repdigit" or "wing" in a strict sense. - M. F. Hasler, Feb 09 2020

Examples

			5 is a term because (10^5 - 1)/9 + 2*10^2 = 11311.
		

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...11311...11
• Index entries for primes involving repunits.

Crossrefs

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

See A332113 for the (prime and composite) near-repunit palindromes 1..131..1.

Programs

Mathematica

Do[ If[ PrimeQ[(10^n + 18*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 20000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A107123(n+1) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018