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

1,1

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)

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A023242, A023272.

Sequence in context: A214124 A103041 A216307 * A006827 A193992 A112346

Adjacent sequences: A176220 A176221 A176222 * A176224 A176225 A176226

Keyword

nonn

Author

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

Extensions

More terms from Michel Marcus, Jun 28 2013

Status

approved