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A176223 Natural numbers k which give a prime by the function f(k) = 2 * k + 13 for at least two iterations.

%I A176223 #12 Nov 20 2020 14:00:42
%S A176223 2,5,8,17,23,35,38,47,50,68,77,80,107,110,113,140,152,170,218,227,233,
%T A176223 245,248,278,287,317,320,332,353,365,380,392,407,437,458,467,485,500,
%U A176223 518,542,575,590,602,605,623,635,638,710,740,743,770,803,827,842
%N A176223 Natural numbers k which give a prime by the function f(k) = 2 * k + 13 for at least two iterations.
%C A176223 n, p = f(k) = 2 * k + 13, q = f(f(k)) = 4 * k + 39; p and q to be primes.
%C A176223 List of (k,p,q):
%C A176223 (2,17,47) (5,23,59) (8,29,71) (17,47,107) (23,59,131)
%C A176223 (35,83,179) (38,89,191) (47,107,227) (50,113,239) (68,149,311)
%C A176223 (77,167,347) (80,173,359) (107,227,467) (110,233,479) (113,239,491)
%C A176223 (140,293,599) (152,317,647) (170,353,719) (218,449,911) (227,467,947)
%C A176223 (233,479,971) (245,503,1019) (248,509,1031) (278,569,1151) (287,587,1187)
%C A176223 (317,647,1307) (320,653,1319) (332,677,1367) (353,719,1451) (365,743,1499)
%H A176223 Daniel Starodubtsev, <a href="/A176223/b176223.txt">Table of n, a(n) for n = 1..10000</a>
%e A176223 2 * 2 + 13 = 17 = prime(7), 4 * 2 + 39 = 47 = prime(15), 2 is first term.
%e A176223 2 * 5 + 13 = 23 = prime(9), 4 * 5 + 39 = 59 = prime(17), 5 is 2nd term.
%t A176223 k13Q[n_]:=AllTrue[Rest[NestList[2#+13&,n,2]],PrimeQ]; Select[Range[ 1000],k13Q] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 20 2020 *)
%o A176223 (PARI) isok(n) = isprime(p=2*n+13) && isprime(2*p+13) \\ _Michel Marcus_, Jun 28 2013
%Y A176223 Cf. A023242, A023272.
%K A176223 nonn
%O A176223 1,1
%A A176223 Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 12 2010
%E A176223 More terms from _Michel Marcus_, Jun 28 2013