A176247 - OEIS

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

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OFFSET

1,1

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.

LINKS

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

EXAMPLE

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).

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A023242, A023272, A176223.