A107126 - OEIS

%I #32 Jan 17 2019 13:44:08

%S 10,14,40,59,160,412,560,1289,1846

%N Numbers n such that (10^(2n+1)+45*10^n-1)/9 is prime.

%C n is in the sequence iff the palindromic number 1(n).6.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m + 1, 16m + 2, 16m + 5, 22m + 1, 22m + 9, etc. (the proof is easy).

%C a(10) > 10^5. - _Robert Price_, Sep 28 2015

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

%H Patrick De Geest, World!Of Numbers, <a href="http://www.worldofnumbers.com/wing.htm#pwp161">Palindromic Wing Primes (PWP's)</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11611.htm#prime">Prime numbers of the form 11...11611...11</a>

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = (A077787(n)-1)/2.

%e 14 is in the sequence because (10^(2*14+1)+45*10^14-1)/9=1(14).6.1(14) = 11111111111111611111111111111 is prime.

%t Do[If[PrimeQ[(10^(2n + 1) + 45*10^n - 1)/9], Print[n]], {n, 2500}]

%t Position[Table[FromDigits[Join[PadRight[{},n,1],{6},PadRight[{},n,1]]],{n,1850}],_?PrimeQ]//Flatten (* _Harvey P. Dale_, Jun 22 2017 *)

%o (PARI) is(n)=ispseudoprime((10^(2*n+1)+45*10^n-1)/9) \\ _Charles R Greathouse IV_, Jun 06 2017

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

%K nonn,base

%O 1,1

%A _Farideh Firoozbakht_, May 19 2005

%E Edited by _Ray Chandler_, Dec 28 2010