A077784 Numbers k such that (10^k - 1)/3 + 2*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

3, 5, 35, 159, 237, 325, 355, 371, 481, 1649, 3641, 4709, 269623

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(13) > 2*10^5. - Robert Price, Apr 03 2016

Examples

			5 is a term because (10^5 - 1)/3 + 2*10^2 = 33533.
		

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 33...33533...33
• Index entries for primes involving repunits.

Crossrefs

Partial sums of S(n, x), for x=1...9: A021823, A000217, A027941, A061278, A089817, A053142, A092521, A076765, A092420.

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

Programs

Mathematica

Do[ If[ PrimeQ[(10^n + 6*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 4800, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183175(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018

a(13) from Robert Price, Aug 03 2024