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%I #15 Apr 03 2023 10:36:09
%S 41,1031,1451,1481,1511,1811,1889,1901,1931,3449,3491,3821,3911,5081,
%T 5441,5849,6101,6131,7151,7349,7901,8969,9221,10691,10709,11171,11471,
%U 11801,12101,12821,12959,13229,14009,14249,14321,14669,14741,15161
%N Initial primes of Cunningham chains of first type with length exactly 3. Primes in A059453 which survive as primes just two "2p+1 iterations", forming chains of exactly 3 terms.
%H Chris Caldwell's Prime Glossary, <a href="https://t5k.org/glossary/page.php?sort=CunninghamChain">Cunningham chains</a>.
%H Warut Roonguthai, <a href="http://web.archive.org/web/20010405230842/http://ksc9.th.com/warut/cunningham.html">Yves Gallot's Proth.exe and Cunningham Chains</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CunninghamChain.html">Cunningham Chain</a>.
%F {(p-1)/2, p, 2p+1, 4p+3, 8p+7} = {composite, prime, prime, prime, composite}
%e 41 is here because 20 and 325 are composites,41,83,167 are primes.
%t ipccQ[n_]:=Module[{c=(n-1)/2},PrimeQ[NestList[2#+1&,c,4]]=={False, True, True, True, False}]; Select[Prime[Range[2000]],ipccQ] (* _Harvey P. Dale_, Nov 10 2014 *)
%Y Cf. A023272, A023302, A023330, A005384, A005385, A059452-A059455, A007700.
%K nonn
%O 0,1
%A _Labos Elemer_, Feb 20 2001
%E Definition corrected by _Alexandre Wajnberg_, Aug 31 2005
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