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

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

Offset

1,1

Comments

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

References

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

Links

Table of n, a(n) for n=1..9.

Example

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

Crossrefs

A000040, A005602, A005603, A176247

Sequence in context: A251526 A325979 A251525 * A031357 A144800 A108250

Adjacent sequences: A176265 A176266 A176267 * A176269 A176270 A176271

Keyword

fini,nonn

Author

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

Status

approved