|
Search: id:A072296
|
|
|
| A072296 |
|
Least number starting a chain of exactly n consecutive even integers that do not have cototient-inverses. |
|
+0
1
|
|
| 10, 50, 532, 2314, 4628, 22578, 115024, 221960, 478302, 3340304, 22527850
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
If the strong Goldbach conjecture (every even number>6 is the sum of at least 2 distinct primes p and q) is true, sequence contains only even values. Since p*q-phi(p*q)=p+q-1 and then every odd number can be expressed as x-phi(x). - Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 03 2002.
|
|
EXAMPLE
|
Neither 50 nor 52 have CoTotient-inverses, and since 50 is the first of the two and the least number with this property, a(2) = 50.
|
|
MATHEMATICA
|
a = Table[0, {5*10^7}]; Do[b = n - EulerPhi[n]; If[ b < 5*10^7 + 1, a[[b/2]]++ ], {n, 2, 615437100}] (* used to find a(7) *) Do[ If[ a[[n]] == a[[n + 1]] == a[[n + 2]] == a[[n + 3]] == a[[n + 4]] == a[[n + 5]] == a[[n + 6]] == 0, Print[n]], {n, 1, 10^6}]
|
|
CROSSREFS
|
Cf. A005278, A051953, A063512 & A063740.
Sequence in context: A060156 A000450 A124872 this_sequence A106041 A124162 A077044
Adjacent sequences: A072293 A072294 A072295 this_sequence A072297 A072298 A072299
|
|
KEYWORD
|
hard,more,nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 12 2002
|
|
|
Search completed in 0.002 seconds
|
