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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 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 * A350853 A080153 A040124 Adjacent sequences:  A320390 A320391 A320392 * A320394 A320395 A320396 KEYWORD nonn AUTHOR Pierandrea Formusa, Dec 10 2018 STATUS approved

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Last modified July 2 14:02 EDT 2022. Contains 355007 sequences. (Running on oeis4.)