1,1

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.

Chris Caldwell's Prime Glossary, Cunningham chains.

G. Löh, Long chains of nearly doubled primes, Math. Comp. vol. 53 no. 188 (1989) pp 751-759.

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.

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 (mathar(AT)strw.leidenuniv.nl), Jul 23 2008

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

Sequence in context: A122707 A057327 A057328 this_sequence A145982 A088362 A045123

Adjacent sequences: A110019 A110020 A110021 this_sequence A110023 A110024 A110025

easy,nonn

Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), Sep 03 2005

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