A086127 - OEIS

%I #9 Oct 15 2013 22:32:14

%S 4889,18059,62639,225527,557093,604973,700703,804077,806903,837077,

%T 1341203,1363403,1932197,2004269,2062703,2284637,2797463,3157379,

%U 3493103,3746399,3995687,4155413,4227893,4493297,5534939,5708603

%N Numbers n such that n remains prime after five iteration of function f[j]=14f[j]+1, at f[1]=prime.

%F {p, 14p+1, 196p+15, 2744p+211, 38416p+2955, 537824p+41371} are all primes, where p at the start is prime.

%e First chain is: {4889,68447,958259,13415627,187818779,2629462907};

%e 10th chain is {837077,11719079,164067107,2296939499,32157152987,450200141819};

%t k=0; m=14; Do[s=Prime[n]; s1=m*s+1; s2=m*s1+1; s3=m*s2+1; s4=m*s3+1; s5=m*s4+1; If[PrimeQ[s]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s3] &&primeQ[s4]&&PrimeQ[s5], k=k+1; Print[{k, n, s, s1, s2, s3, s4, s5}]], {n, 1, 1000000}]

%t Select[Range[6000000],And@@PrimeQ[NestList[14#+1&,#,5]]&] (* _Harvey P. Dale_, Sep 17 2012 *)

%Y Cf. A085956, A086361, A086362, A023330, A059766, A023287, A000668, A076481.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 23 2003