

A107127


Numbers n such that (10^(2n+1)+54*10^n1)/9 is prime.


44




OFFSET

1,2


COMMENTS

n is in the sequence iff the palindromic number 1(n).7.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+1, 6m, 6m+2, 7m+2, 16m+9, 16m+14, 18m+1, 18m+7, 22m+13, 22m+19, etc. (the proof is easy).
a(9) > 10^5.  Robert Price, Apr 30 2017


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..8.
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 11...11711...11
Index entries for primes involving repunits.


FORMULA

a(n) = (A077789(n)1)/2.


EXAMPLE

3 is in the sequence because (10^(2*3+1)+54*10^31)/9=1(3).7.1(3)=1117111 is prime.
2933 is in the sequence because (10^(2*2933+1)+54*10^29331)/9=1(2933).7.1(2933) is prime.


MATHEMATICA

Do[If[PrimeQ[(10^(2n + 1) + 54*10^n  1)/9], Print[n]], {n, 3250}]


PROG

(PARI) for(n=0, 1e4, if(ispseudoprime(t=(10^(2*n+1)+54*10^n)\9), print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011


CROSSREFS

Cf. A004023, A077775A077798, A107123A107127, A107648, A107649, A115073, A183174A183187.
Sequence in context: A180416 A043038 A274264 * A207323 A135697 A226508
Adjacent sequences: A107124 A107125 A107126 * A107128 A107129 A107130


KEYWORD

nonn,more,base


AUTHOR

Farideh Firoozbakht, May 19 2005


EXTENSIONS

Edited by Ray Chandler, Dec 28 2010
a(6)a(8) from Robert Price, Apr 30 2017


STATUS

approved



