A107649 - OEIS

%I #37 Jan 30 2025 17:21:20

%S 1,4,26,187,226,874,13309,34016,42589

%N Numbers n such that (10^(2n+1)+72*10^n-1)/9 is prime.

%C n is in the sequence iff the palindromic number 1(n).9.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m+5, 22m+3, 22m+7, etc. (the proof is easy).

%C a(10) > 200000. - __Robert Price_, Jan 30 2025

%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#pwp191">Palindromic Wing Primes (PWP's)</a>

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/1/11911.htm#prime">Prime numbers of the form 11...11911...11</a>

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

%F a(n) = (A077795(n)-1)/2.

%e 26 is in the sequence because (10^(2*26+1)+72*10^26-1)/9=1(26).9.1(26)

%e = 11111111111111111111111111911111111111111111111111111 is prime.

%t Do[If[PrimeQ[(10^(2n + 1) + 72*10^n - 1)/9], Print[n]], {n, 3000}]

%t prQ[n_]:=Module[{c=PadRight[{},n,1]},PrimeQ[FromDigits[Join[c,{9},c]]]]; Select[Range[13500],prQ] (* _Harvey P. Dale_, Jan 19 2014 *)

%o (PARI) for(n=0,1e4,if(ispseudoprime(t=(10^(2*n+1)+72*10^n)\9),print1(t", "))) \\ _Charles R Greathouse IV_, Jul 15 2011

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

%K nonn,more,base

%O 1,2

%A _Farideh Firoozbakht_, May 19 2005

%E Edited by _Ray Chandler_, Dec 28 2010

%E a(8)-a(9) from _Robert Price_, Sep 28 2017