|
| |
|
|
A059763
|
|
Primes starting a Cunningham chain of the first kind of length 4.
|
|
13
|
|
|
|
509, 1229, 1409, 2699, 3539, 6449, 10589, 11549, 11909, 12119, 17159, 19709, 19889, 22349, 26189, 27479, 30389, 43649, 55229, 57839, 60149, 71399, 74699, 75329, 82499, 87539, 98369, 101399, 104369, 112919, 122099, 139439, 148829, 166739
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Initial (unsafe) primes of Cunningham chains of first type with length exactly 4. Primes in A059453 which survive as primes just three "2p+1 iterations", forming chains of exactly 4 terms.
The definition indicates each chain is exactly 4 primes long (i.e., the chain cannot be a subchain of a longer one). That's why this sequence is different from A023272, which also gives primes included in longer chains ("starting" them or not).
|
|
|
LINKS
|
|
|
|
FORMULA
|
{(p-1)/2, p, 2p+1, 4p+3, 8p+7, 16p+15} = {composite, prime, prime, prime, prime, composite}.
|
|
|
EXAMPLE
|
1229 is here because, through 2p+1, 1229 -> 2459 -> 4919 -> 9839 and the chain ends here since 2*9839 + 1 = 11*1789 is composite.
|
|
|
MAPLE
|
isA059763 := proc(p) local pitr, itr ; if isprime(p) then if isprime( (p-1)/2 ) then RETURN(false) ; else pitr := p ; for itr from 1 to 3 do pitr := 2*pitr+1 ; if not isprime(pitr) then RETURN(false) ; fi ; od: pitr := 2*pitr+1 ; if isprime(pitr) then RETURN(false) ; else RETURN(true) ; fi ; fi ; else RETURN(false) ; fi ; end: for i from 2 to 100000 do p := ithprime(i) ; if isA059763(p) then printf("%d, ", p) ; fi ; od: # R. J. Mathar, Jul 23 2008
|
|
|
CROSSREFS
|
Cf. A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326.
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
Edited and extended by R. J. Mathar, Jul 23 2008, Aug 18 2008
|
|
|
STATUS
|
approved
|
| |
|
|
