%I #20 Mar 15 2020 04:02:31

%S 2,5,17,23,47,107,113,227,233,317,353,467,743,827,1013,1163,1223,1283,

%T 1493,1697,1823,1877,2063,2333,2543,2957,3323,3467,3767,3797,4013,

%U 4397,4523,5297,5393,5507,5693,5717,5897,5927,6053,6317,6473,6737,6947,6977

%N Primes p which give a prime iterated by f(p) = 2*p + 13 for at least two steps.

%C Subsequence of A176223.

%C p, f(p) = 2*p + 13, q = f(f(p)) = 4*p + 39 to be primes.

%C Necessarily for such primes p > 5, the LSD (least significant digit) is either 3 or 7, since an LSD of 1 gives the LSD of f(p) equal to 5 and an LSD of 9 gives the LSD of f(f(p)) equal to 5.

%H Daniel Starodubtsev, <a href="/A176247/b176247.txt">Table of n, a(n) for n = 1..10000</a>

%e f(2) = 17 = prime(7), f(17) = 47 = prime(15), 2 is first term.

%e f(5) = 23 = prime(9), f(23) = 59 = prime(17), 5 is 2nd term.

%e Note first resulting palindromic prime: f(3323) = 6659 = prime(858), q = 13331 = prime(1583) = palprime(29).

%t Select[Prime@ Range[10^3], AllTrue[NestList[2 # + 13 &, #, 2], PrimeQ] &] (* _Michael De Vlieger_, Mar 14 2020 *)

%o (PARI) isok(n) = isprime(n) && isprime(p=2*n+13) && isprime(2*p+13) \\ _Michel Marcus_, Jun 28 2013

%Y Cf. A023242, A023272, A176223.

%K nonn

%O 1,1

%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 13 2010

%E More terms from _Michel Marcus_, Jun 28 2013