A176247 Primes p which give a prime iterated by f(p) = 2*p + 13 for at least two steps.

2, 5, 17, 23, 47, 107, 113, 227, 233, 317, 353, 467, 743, 827, 1013, 1163, 1223, 1283, 1493, 1697, 1823, 1877, 2063, 2333, 2543, 2957, 3323, 3467, 3767, 3797, 4013, 4397, 4523, 5297, 5393, 5507, 5693, 5717, 5897, 5927, 6053, 6317, 6473, 6737, 6947, 6977

Offset: 1

Author

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

Keywords

• nonn

Comments

Subsequence of A176223.

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

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.

Examples

			f(2) = 17 = prime(7), f(17) = 47 = prime(15), 2 is first term.
f(5) = 23 = prime(9), f(23) = 59 = prime(17), 5 is 2nd term.
Note first resulting palindromic prime: f(3323) = 6659 = prime(858), q = 13331 = prime(1583) = palprime(29).
		

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023242, A023272, A176223.

Programs

Mathematica

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

PARI

isok(n) = isprime(n) && isprime(p=2*n+13) && isprime(2*p+13) \\ Michel Marcus, Jun 28 2013

Extensions

More terms from Michel Marcus, Jun 28 2013