The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A077775 Odd 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) of the form 3...313...3. 47
 3, 7, 15, 123, 181, 185, 539, 597, 643, 743, 1553, 3135, 4769, 5133, 6177, 11733, 16103, 18997, 25271, 49025, 65043, 87965 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Prime versus probable prime status and proofs are given in the author's table. a(23) > 2*10^5. - Robert Price, Jan 29 2016 Primes of the form (10^k-1)/3 - 2*10^floor(k/2) are obtained for k in (2, 3, 6, 7, 8, 10, 15, 22, 34, 123, 126, 144, 181, 185, 198, 534, 539, 597, 606, ...). For example (10^2 - 1)/3 - 2*10^1 = 13 is also prime. However, for even k the result is not palindromic. See A077775-A077798, A107123-A107127 for PWP's with digits other than 3 and 1. - M. F. Hasler, Mar 03 2019 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...33133...33 FORMULA a(n) = 2*A183174(n) + 1. EXAMPLE a(3) = 15 corresponds to the prime (10^15 - 1)/3 - 2*10^7 = 333333313333333. MATHEMATICA Do[ If[ PrimeQ[(10^n - 6*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 49100, 2}] (* Robert G. Wilson v, Dec 16 2005 *) PROG (PARI) is(n)=bittest(n, 0)&&ispseudoprime(10^n\3-2*10^(n\2)) \\ M. F. Hasler, Mar 03 2019 CROSSREFS Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187. Sequence in context: A154795 A193831 A246719 * A197594 A206851 A033089 Adjacent sequences:  A077772 A077773 A077774 * A077776 A077777 A077778 KEYWORD more,nonn,base AUTHOR Patrick De Geest, Nov 16 2002 EXTENSIONS a(21)-a(22) from Robert Price, Jan 29 2016 a(21) corrected by Robert Price, Feb 03 2016 Name corrected by Jon E. Schoenfield, Oct 31 2018 Name edited by M. F. Hasler, Mar 03 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 17 19:36 EDT 2021. Contains 343988 sequences. (Running on oeis4.)