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A320393 First members of the Cunningham chains of the first kind whose length is a prime.

%I A320393 #30 Jan 23 2019 10:54:01
%S A320393 2,3,11,23,29,41,53,83,113,131,173,179,191,233,239,251,281,293,419,
%T A320393 431,443,491,593,641,653,659,683,719,743,761,809,911,953,1013,1019,
%U A320393 1031,1049,1103,1223,1289,1439,1451,1481,1499,1511,1559,1583,1601,1733,1811,1889,1901,1931,1973,2003,2039,2063,2069,2129,2141
%N A320393 First members of the Cunningham chains of the first kind whose length is a prime.
%e A320393 41 is an item as it generates the Cunningham chain (41, 83, 167), of length 3, that is prime.
%t A320393 aQ[n_] := PrimeQ[Length[NestWhileList[2#+1&, n, PrimeQ]] - 1]; Select[Range[2200], aQ] (* _Amiram Eldar_, Dec 11 2018 *)
%o A320393 (Python)
%o A320393 from sympy.ntheory import isprime
%o A320393 def cunningham_chain(p,t):
%o A320393     #it returns the cunningham chain generated by p of type t (1 or 2)
%o A320393     if not(isprime(p)):
%o A320393         raise Exception("Invalid starting number! It must be prime")
%o A320393     if t!=1 and t!=2:
%o A320393         raise Exception("Invalid type! It must be 1 or 2")
%o A320393     elif t==1: k=t
%o A320393     else: k=-1
%o A320393     cunn_ch=[]
%o A320393     cunn_ch.append(p)
%o A320393     while isprime(2*p+k):
%o A320393         p=2*p+k
%o A320393         cunn_ch.append(p)
%o A320393     return(cunn_ch)
%o A320393 from sympy import prime
%o A320393 n=350
%o A320393 r=""
%o A320393 for i in range(1,n):
%o A320393     cunn_ch=(cunningham_chain(prime(i),1))
%o A320393     lcunn_ch=len(cunn_ch)
%o A320393     if isprime(lcunn_ch):
%o A320393        r += ","+str(prime(i))
%o A320393 print(r[1:])
%Y A320393 Cf. A059761, A059762, A059764.
%K A320393 nonn
%O A320393 1,1
%A A320393 _Pierandrea Formusa_, Dec 10 2018