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%I #23 Jul 15 2024 10:23:36
%S 509,1229,1409,2699,3539,6449,10589,11549,11909,12119,17159,19709,
%T 19889,22349,26189,27479,30389,43649,55229,57839,60149,71399,74699,
%U 75329,82499,87539,98369,101399,104369,112919,122099,139439,148829,166739
%N Primes starting a Cunningham chain of the first kind of length 4.
%C 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.
%C 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).
%C Prime p such that {(p-1)/2, p, 2p+1, 4p+3, 8p+7, 16p+15} = {composite, prime, prime, prime, prime, composite}.
%H Amiram Eldar, <a href="/A059763/b059763.txt">Table of n, a(n) for n = 1..10000</a>
%H Chris Caldwell's Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=CunninghamChain">Cunningham chains</a>.
%e 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.
%p 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
%Y Cf. A023272, A023302, A023330, A005384, A005385, A059452, A059455, A007700.
%Y Cf. A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326.
%K easy,nonn
%O 1,1
%A _Labos Elemer_, Feb 20 2001
%E Edited and extended by _R. J. Mathar_, Jul 23 2008, Aug 18 2008
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