A110022 Primes starting a Cunningham chain of the second kind of length 5.

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

Offset: 1

Author

Alexandre Wajnberg, Sep 03 2005

Keywords

• easy
• nonn

Comments

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.

Examples

			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.
		

Links

• 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.

Crossrefs

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

Programs

Maple

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

Extensions

Edited and extended by R. J. Mathar, Jul 23 2008