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A110022
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Primes starting a Cunningham chain of the second kind of length 5.
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4
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1531, 6841, 15391, 44371, 57991, 83431, 105871, 145021, 150151, 199621, 209431, 212851, 231241, 242551, 291271, 319681, 346141, 377491, 381631, 451411, 481021, 506791, 507781, 512821, 537811, 588871, 680431, 727561, 749761, 782911, 787711
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OFFSET
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1,1
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COMMENTS
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The definition indicates that each chain is exactly 5 primes long (i.e. the chain cannot be a subchain of a longer one). That's why this sequence is different from A057328 which gives also primes included in longer chains (thus not "starting" them), as 16651, starting a seven primes chain, or 33301, second prime of the same seven primes chain.
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LINKS
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EXAMPLE
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6841 is here because: 6841 through <2p-1> -> 13681-> 27361-> 54721-> 109441 and the chain ends here since 2*109441-1=13*113*149 is composite.
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MAPLE
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isA110022 := 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 4 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 200000 do p := ithprime(i) ; if isA110022(p) then printf("%d, ", p) ; fi ; od: # R. J. Mathar, Jul 23 2008
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CROSSREFS
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Cf. A023272, A023302, A023330, A005384, A005385, A059452, A059455, A007700, A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326.
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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