A320342 Maximum term in Cunningham chain of the first kind generated by the n-th prime.

47, 7, 47, 7, 47, 13, 17, 19, 47, 59, 31, 37, 167, 43, 47, 107, 59, 61, 67, 71, 73, 79, 167, 2879, 97, 101, 103, 107, 109, 227, 127, 263, 137, 139, 149, 151, 157, 163, 167, 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

Offset: 1

Author

Pierandrea Formusa, Dec 10 2018

Keywords

• nonn

Comments

No term is a Sophie Germain prime.

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

Examples

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

Crossrefs

Cf. A181697.

Programs

Mathematica

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

Python

def cunningham_chain(p,t):
    # returns the Cunningham chain generated by p of type t (1 or 2)
    from sympy.ntheory import isprime
    if not(isprime(p)):
        raise Exception("Invalid starting number! It must be prime")
    if t!=1 and t!=2:
        raise Exception("Invalid type! It must be 1 or 2")
    elif t==1: k=t
    else: k=-1
    cunn_ch=[]
    cunn_ch.append(p)
    while isprime(2*p+k):
        p=2*p+k
        cunn_ch.append(p)
    return(cunn_ch)
from sympy import prime
n=71
r=""
for i in range(1,n):
    cunn_ch=(cunningham_chain(prime(i),1))
    last_item=cunn_ch[-1]
    r += ","+str(last_item)
print(r[1:])