

A224887


Honaker trios: Consecutive prime numbers p < q < r such that p  (qr+1).


0




OFFSET

1,1


COMMENTS

The primes p, q, r are listed as a(3n2), a(3n1), a(3n) for n = 1, 2, 3, ...
Caldwell & Cheng show that there are only 3 Honaker trios below 2*10^17 and that these are the only Honaker trios if the CramérGranville conjecture is satisfied with a constant M < 199262; they also give other sufficient conditions for the number of Honaker trios to be finite.
Strictly speaking, the keywords "fini,full" are thus only conjectured, but given that the CramérGranville conjecture is believed to hold with M = 2*exp(gamma) ~ 1.123, it seems justified to use them.


REFERENCES

R. Crandall and C. Pomerance, Prime Numbers  A Computational Perspective, SpringerVerlag, New York, 2001, p. 73.


LINKS

Table of n, a(n) for n=1..9.
Chris K. Caldwell, Yuanyou Cheng, Determining Mills' Constant and a Note on Honaker's Problem, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.1


MATHEMATICA

Flatten[Select[Partition[Prime[Range[50]], 3, 1], Divisible[Times@@ Rest[ #]+1, #[[1]]]&]] (* Harvey P. Dale, Feb 03 2015 *)


PROG

(PARI) forprime(p=3, default(primelimit), (nextprime(p+1)*p+1)%precprime(p1)print1(precprime(p1)", "p", "nextprime(p+1)", ")) \\ For PARI/GP version >= 2.6, default(primelimit) can be omitted.


CROSSREFS

Sequence in context: A083776 A122820 A261324 * A151571 A193957 A336746
Adjacent sequences: A224884 A224885 A224886 * A224888 A224889 A224890


KEYWORD

nonn,fini,full


AUTHOR

M. F. Hasler, Jul 24 2013


STATUS

approved



