A086126 Duplicate of A023287.
61, 101, 1811, 3491, 4091, 5711, 5801, 6361, 7121, 10391, 10771, 11311, 13421, 15131
Offset: 1
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
[n: n in [0..100000] | IsPrime(n) and IsPrime(6*n+1) and IsPrime(36*n+7)] // Vincenzo Librandi, Aug 04 2010
Select[Prime[Range[800]],AllTrue[Rest[NestList[6#+1&,#,2]],PrimeQ]&] (* Harvey P. Dale, Oct 17 2020 *)
lista(nn) = forprime(n=1, nn, if (isprime(p=6*n+1) && isprime(6*p+1), print1(n, ", "))); \\ Michel Marcus, Oct 17 2015
First chain is {831167, 6649337, 53194697, 425557577, 3404460617, 27235684937};
If p is congruent to {1,3,7,9} mod 10, then consecutive iterates are congruent to {9,5,7,3}, {3,1,7,5}, {5,9,7,1} respectively; so only 10k+7 may remain prime through five iterations, as sequence demonstrates nicely. - _Labos Elemer_, Jul 23 2003
k=0; m=8; 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}]
it5Q[n_]:=AllTrue[Rest[NestList[8#+1&,n,5]],PrimeQ]; Select[Prime[Range[ 9*10^6]],it5Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 12 2014 *)
First chain is: {4889,68447,958259,13415627,187818779,2629462907}.
10th chain is {837077,11719079,164067107,2296939499,32157152987,450200141819}.
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 *)
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