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A320393 First members of the Cunningham chains of the first kind whose length is a prime. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

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

MATHEMATICA

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

PROG

(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:])

CROSSREFS

Cf. A059761, A059762, A059764.

Sequence in context: A236168 A235634 A070174 * A080153 A040124 A082739

Adjacent sequences:  A320390 A320391 A320392 * A320394 A320395 A320396

KEYWORD

nonn

AUTHOR

Pierandrea Formusa, Dec 10 2018

STATUS

approved

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Last modified February 25 12:01 EST 2020. Contains 332233 sequences. (Running on oeis4.)