

A235364


Twin primes p, p+2 such that p+1 is a Giuga number.


2




OFFSET

1,1


COMMENTS

For all 12 known Giuga numbers N, either both N1 and N+1 are prime or neither is prime. Is it true that if any Giuga number N is adjacent to a prime N1 or N+1, then in fact N lies between twin primes N1, N+1?
See A235139 for a similar property of the known primary pseudoperfect numbers.
A007850 lists a 13th in its comments.  Bill McEachen, Jan 14 2014
If g = 420001794970774706203871150967065663240419575375163060922876441614\ 2557211582098432545190323474818 is confirmed as the 13th Giuga number, it will not be between a(7) and a(8), because g1 is divisible by 13. So a(7) is not equal to g1. But g+1 is prime (certified using the APRCL test in Pari) so g provides a negative answer to the above question.  Ralf Stephan, Jan 20 2014 (corrected by Jonathan Sondow, Jan 21 2014)
(Revision of my question.) For all 13 known Giuga numbers N, if N1 is prime, then N+1 is also prime. Is it true that if any Giuga number N is 1 more than a prime, then N lies between twin primes N1, N+1?  Jonathan Sondow, Mar 02 2014


LINKS

Table of n, a(n) for n=1..6.
MathWorld, Giuga Number
Wikipedia, Giuga number


EXAMPLE

For the twin primes (p,p+2) = (29, 31), (857, 859), (1721, 1723), the numbers p+1 = 30, 858, 1722 are Giuga numbers (A007850).


CROSSREFS

Cf. A007850, A235139.
Sequence in context: A288615 A158342 A077286 * A178425 A294737 A261521
Adjacent sequences: A235361 A235362 A235363 * A235365 A235366 A235367


KEYWORD

nonn,more,hard


AUTHOR

Jonathan Sondow, Jan 07 2014


STATUS

approved



