|
Search: id:A023287
|
|
|
| A023287 |
|
Numbers n such that n remains prime through 3 iterations of function f(x) = 6x + 1. |
|
+0
4
|
|
| 61, 101, 1811, 3491, 4091, 5711, 5801, 6361, 7121, 10391, 10771, 11311, 13421, 15131, 17791, 18911, 19471, 20011, 24391, 25601, 25951, 30091, 35251, 41911, 45631, 47431, 55631, 58711, 62921, 67891, 70451, 70571, 72271, 74051, 74161, 75431, 80471, 86341
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Primes p such that s1=p, s2=6s1+1, s3=6s2+1 and also s4=6s3+1 are primes forming a special chain of four primes. Fifth term in such a chain cannot arise. See A085956, A086361, A086362.
|
|
FORMULA
|
{p, 6p+1, 36p+7, 216p+43} are all primes, where p is prime.
|
|
EXAMPLE
|
First chain is: {61,367,2203,13219}; 319th chain is {1291391,7748347,46490083,278940499}; entries in chains are congruent to {1,7,3,9} mod 10.
|
|
MATHEMATICA
|
k=0; m=6; Do[s=Prime[n]; s1=m*s+1; s2=m*s1+1; s3=m*s2+1; If[PrimeQ[s]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s3], k=k+1; Print[{k, n, s, s1, s2, s3}]], {n, 1, 100000}]
|
|
CROSSREFS
|
Cf. A085956, A086361, A086362, A023330, A059766.
Sequence in context: A106390 A142191 A086126 this_sequence A141919 A141301 A107152
Adjacent sequences: A023284 A023285 A023286 this_sequence A023288 A023289 A023290
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
David W. Wilson (davidwwilson(AT)comcast.net)
|
|
EXTENSIONS
|
Additional comments from Labos E. (labos(AT)ana.sote.hu), Jul 23 2003
|
|
|
Search completed in 0.002 seconds
|
