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