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

1,1

Comments

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

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

References

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Table of n, a(n) for n=1..14.

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.

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A229527 A091711 A103007 * A322971 A165469 A160160

Adjacent sequences: A077787 A077788 A077789 * A077791 A077792 A077793

Keyword

more,nonn,base

Author

Patrick De Geest, Nov 16 2002

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018

a(14) from Robert Price, Oct 30 2023

Status

approved