A320342 - OEIS

%I #41 Jan 27 2019 08:58:29

%S 47,7,47,7,47,13,17,19,47,59,31,37,167,43,47,107,59,61,67,71,73,79,

%T 167,2879,97,101,103,107,109,227,127,263,137,139,149,151,157,163,167,

%U 347,2879,181,383,193,197,199,211,223,227,229,467,479,241,503,257,263,269,271,277,563,283,587,307,311,313,317,331,337,347,349

%N Maximum term in Cunningham chain of the first kind generated by the n-th prime.

%C No term is a Sophie Germain prime.

%C A181697 is the sequence of the lengths of the chains in the name.

%e a(1)=47 as prime(1)=2 and the Cunningham chain generated by 2 is (2,5,11,23,47), with maximum item 47.

%t a[n_] := NestWhile[2#+1&, n, PrimeQ, 1, Infinity, -1]; a/@Prime@Range@70  (* _Amiram Eldar_, Dec 11 2018 *)

%o (Python)

%o def cunningham_chain(p,t):

%o     # returns the Cunningham chain generated by p of type t (1 or 2)

%o     from sympy.ntheory import isprime

%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=71

%o r=""

%o for i in range(1,n):

%o     cunn_ch=(cunningham_chain(prime(i),1))

%o     last_item=cunn_ch[-1]

%o     r += ","+str(last_item)

%o print(r[1:])

%Y Cf. A181697.

%K nonn

%O 1,1

%A _Pierandrea Formusa_, Dec 10 2018