A086127 Numbers n such that n remains prime after five iteration of function f[j]=14f[j]+1, 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

1,1

Links

Table of n, a(n) for n=1..26.

Formula

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

Example

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

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[{k, n, s, s1, s2, s3, s4, s5}]], {n, 1, 1000000}]
Select[Range[6000000], And@@PrimeQ[NestList[14#+1&, #, 5]]&] (* Harvey P. Dale, Sep 17 2012 *)

Crossrefs

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

Sequence in context: A210385 A075294 A206273 * A126704 A251325 A186478

Adjacent sequences: A086124 A086125 A086126 * A086128 A086129 A086130

Keyword

nonn

Author

Labos Elemer, Jul 23 2003

Status

approved