A086127 Numbers k such that k remains prime after five iteration of function f(j) = 14*f(j)+1, starting at f(1) = prime.

4889, 18059, 62639, 225527, 557093, 604973, 700703, 804077, 806903, 837077, 1341203, 1363403, 1932197, 2004269, 2062703, 2284637, 2797463, 3157379, 3493103, 3746399, 3995687, 4155413, 4227893, 4493297, 5534939, 5708603

Offset: 1

Author

Labos Elemer, Jul 23 2003

Keywords

• nonn

Comments

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

Examples

			First chain is: {4889,68447,958259,13415627,187818779,2629462907}.
10th chain is {837077,11719079,164067107,2296939499,32157152987,450200141819}.
		

Crossrefs

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

Programs

Mathematica

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[s]], {n, 1, 1000000}]
Select[Range[6000000],And@@PrimeQ[NestList[14#+1&,#,5]]&] (* Harvey P. Dale, Sep 17 2012 *)