1,1

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 gives also primes included in longer chains ("starting" them or not).

Chris Caldwell's Prime Glossary, Cunningham chains.

{(p-1)/2, p, 2p+1, 4p+3, 8p+7, 16p+15} = {composite, prime, prime, prime, prime, composite}

1229 is here because, through 2p+1, 1229 -> 2459 -> 4919 -> 9839 and the chain ends here since 2*9839+1=11*1789 is composite.

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

Cf. A023272, A023302, A023330, A005384, A005385, A059452, A059455, A007700, Cf. A059759, A059760, A059761, A059762, A059763, A059764, A059765, A038397, A104349, A091314, A069362, A016093, A014937, A057326.

Sequence in context: A159686 A142819 A110025 this_sequence A126438 A126582 A062905

Adjacent sequences: A059760 A059761 A059762 this_sequence A059764 A059765 A059766

easy,nonn

Labos E. (labos(AT)ana.sote.hu), Feb 20 2001

Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 23 2008, Aug 18 2008