A176223 -id:A176223 - cp's OEIS frontend

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

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

nonn

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.

			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).

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

Cf. A023242, A023272, A176223.

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

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

More terms from Michel Marcus, Jun 28 2013

A176268 Primes of a Generalized Cunningham chain of length 9 by the function f(p) = 2 * p + 13.

Original entry on oeis.org

3467, 6947, 13907, 27827, 55667, 111347, 222707, 445427, 890867

Offset: 1

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

See comments and references of A176223 and A176247
Chain of 8 primes: 2, 17, 47, 107, 227, 467, 947, 1907
It is conjectured that arbitrarily long such chains exist

			3467 = prime(486), (3467 - 13)/ 2 = 1727 = 11 * 157 is composite
f(3467) = 6947 = prime(891), f(6947) = 13907 = prime(1644)
f(13907) = 27827 = prime(3040), f( 27827) = 55667 = prime(5649)
f(55667) = 111347 = prime(10565), f(111347) = 222707 = prime(19832)
f(222707) = 445427 = prime(37374), f(445427) = 890867 = prime(70612)
f(890867) = 1781747 = 11 * 161977
3467 is smallest prime for such a chain of 9 primes

Joe Buhler: Algorithmic Number Theory: Third International Symposium, ANTS-III, New York: Springer, 1998
David J. Darling: The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes, Hoboken: John Wiley & Sons, 2004
Paulo Ribenboim: Die Welt der Primzahlen. Geheimnisse und Rekorde, Springer-Verlag GmbH & Co. KG, 2006

A000040, A005602, A005603, A176247

cp's OEIS Frontend

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

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