

A107124


Numbers n such that (10^(2n+1)+27*10^n1)/9 is prime.


3




OFFSET

1,1


COMMENTS

n is in the sequence iff the palindromic number 1(n).4.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+1, 16m+11, 16m+12, 18m+11, 18m+15, etc. (the proof is easy).


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..5.
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 11...11411...11
Index entries for primes involving repunits.


FORMULA

a(n) = (A077780(n)1)/2.


EXAMPLE

32 is in the sequence because the palindromic number (10^(2*32+1)+27*10^321)/9 = 1(32).4.1(32) =
11111111111111111111111111111111411111111111111111111111111111111 is prime.


MATHEMATICA

Do[If[PrimeQ[(10^(2n + 1) + 27*10^n  1)/9], Print[n]], {n, 2200}]
Select[Range[1600], PrimeQ[FromDigits[Join[PadRight[{}, #, 1], {4}, PadRight[ {}, #, 1]]]]&] (* Harvey P. Dale, Aug 01 2017 *)


PROG

(PARI) is(n)=ispseudoprime((10^(2*n+1)+27*10^n1)/9) \\ Charles R Greathouse IV, May 22 2017


CROSSREFS

Cf. A004023, A077775A077798, A107123A107127, A107648, A107649, A115073, A183174A183187.
Sequence in context: A041053 A212763 A103108 * A141049 A052830 A041895
Adjacent sequences: A107121 A107122 A107123 * A107125 A107126 A107127


KEYWORD

nonn,base,more


AUTHOR

Farideh Firoozbakht, May 19 2005


EXTENSIONS

Edited by Ray Chandler, Dec 28 2010


STATUS

approved



