OFFSET
1,1
COMMENTS
Initial (unsafe) primes of Cunningham chains of first type with length exactly 4. Primes in A059453 that 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 is why this sequence is different from A023272, which also gives primes included in longer chains ("starting" them or not).
Prime p such that {(p-1)/2, p, 2p+1, 4p+3, 8p+7, 16p+15} = {composite, prime, prime, prime, prime, composite}.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Chris Caldwell's Prime Glossary, Cunningham chains.
EXAMPLE
1229 is a term 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
KEYWORD
easy,nonn
AUTHOR
Labos Elemer, Feb 20 2001
EXTENSIONS
Edited and extended by R. J. Mathar, Jul 23 2008, Aug 18 2008
STATUS
approved