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

2, 5, 8, 17, 23, 35, 38, 47, 50, 68, 77, 80, 107, 110, 113, 140, 152, 170, 218, 227, 233, 245, 248, 278, 287, 317, 320, 332, 353, 365, 380, 392, 407, 437, 458, 467, 485, 500, 518, 542, 575, 590, 602, 605, 623, 635, 638, 710, 740, 743, 770, 803, 827, 842

Offset: 1

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Apr 12 2010

Keywords

• nonn

Comments

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

List of (k,p,q):

(2,17,47) (5,23,59) (8,29,71) (17,47,107) (23,59,131)

(35,83,179) (38,89,191) (47,107,227) (50,113,239) (68,149,311)

(77,167,347) (80,173,359) (107,227,467) (110,233,479) (113,239,491)

(140,293,599) (152,317,647) (170,353,719) (218,449,911) (227,467,947)

(233,479,971) (245,503,1019) (248,509,1031) (278,569,1151) (287,587,1187)

(317,647,1307) (320,653,1319) (332,677,1367) (353,719,1451) (365,743,1499)

Examples

			2 * 2 + 13 = 17 = prime(7), 4 * 2 + 39 = 47 = prime(15), 2 is first term.
2 * 5 + 13 = 23 = prime(9), 4 * 5 + 39 = 59 = prime(17), 5 is 2nd term.
		

Links

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

Crossrefs

Cf. A023242, A023272.

Programs

Mathematica

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 *)

PARI

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

Extensions

More terms from Michel Marcus, Jun 28 2013