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

2, 3, 11, 23, 29, 41, 53, 83, 113, 131, 173, 179, 191, 233, 239, 251, 281, 293, 419, 431, 443, 491, 593, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1013, 1019, 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

Offset: 1

Author

Pierandrea Formusa, Dec 10 2018

Keywords

• nonn

Examples

			41 is an item as it generates the Cunningham chain (41, 83, 167), of length 3, that is prime.
		

Crossrefs

Cf. A059761, A059762, A059764.

Programs

Mathematica

aQ[n_] := PrimeQ[Length[NestWhileList[2#+1&, n, PrimeQ]] - 1]; Select[Range[2200], aQ] (* Amiram Eldar, Dec 11 2018 *)

Python

from sympy.ntheory import isprime
def cunningham_chain(p,t):
    #it returns the cunningham chain generated by p of type t (1 or 2)
    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=350
r=""
for i in range(1,n):
    cunn_ch=(cunningham_chain(prime(i),1))
    lcunn_ch=len(cunn_ch)
    if isprime(lcunn_ch):
       r += ","+str(prime(i))
print(r[1:])