

A077775


Odd numbers k such that (10^k  1)/3  2*10^floor(k/2) is a palindromic wing prime (a.k.a. nearrepdigit 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
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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^k1)/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 A077775A077798, A107123A107127 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, 199697, pp. 19.


LINKS

Table of n, a(n) for n=1..22.
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 33...33133...33
Index entries for primes involving repunits.


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\32*10^(n\2)) \\ M. F. Hasler, Mar 03 2019


CROSSREFS

Cf. A004023, A077775A077798, A107123A107127, A107648, A107649, A115073, A183174A183187.
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



