A077790 Numbers k such that (10^k - 1)/3 + 4*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

3, 7, 15, 23, 27, 35, 59, 63, 67, 155, 1867, 3111, 23517, 235415

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(14) > 200000. - Robert Price, Dec 29 2016

Examples

			23 is a term because (10^23 - 1)/3 + 4*10^11 = 33333333333733333333333.
		

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...33733...33
• 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 + 12*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 23600, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A183176(n) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018

a(14) from Robert Price, Oct 30 2023