|
Search: id:A135928
|
|
|
| A135928 |
|
Digital roots of the Mersenne primes. |
|
+0
3
|
|
| 3, 7, 4, 1, 1, 4, 1, 1, 1, 4, 4, 1, 4, 1, 1, 1, 1, 1, 4, 1, 4, 4, 4, 4, 4, 1, 1, 4, 1, 1, 1, 4, 4, 1, 4, 4, 4, 4, 1
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
As a consequence of the fact that all prime numbers are of the form 6n-1 or 6n+1 for p>3, all the elements of this sequence after the second will be either 1 or 4, although there is no obvious pattern to their distribution. We can use this result to show that all Mersenne primes after the first are congruent to 1, modulo 6. This sequence is complete as far as the 39th term.
|
|
REFERENCES
|
Asadulla, Syed; Digital Roots of Mersenne Primes and Even Perfect Numbers, The College Mathematics Journal, Vol. 15, No. 1. (1984), pp. 53-54.
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Digital Root.
|
|
FORMULA
|
a(n)=digital root of A000668(n).
|
|
EXAMPLE
|
The fourth Mersenne prime is 127, which has a digital root of 1. Hence a(4)=1.
|
|
MATHEMATICA
|
DigitalRoot[n_]:=FixedPoint[Plus@@IntegerDigits[ # ]&, n]; data1=Select[Range[4500], PrimeQ[2^#-1] &]; data2=2^#-1 &/@data1; DigitalRoot/@data2
|
|
CROSSREFS
|
Cf. A000668, A000043, A003010, A001566, A135927.
Sequence in context: A050393 A110778 A108297 this_sequence A011444 A010471 A077226
Adjacent sequences: A135925 A135926 A135927 this_sequence A135929 A135930 A135931
|
|
KEYWORD
|
hard,nonn,base
|
|
AUTHOR
|
Ant King (mathstutoring(AT)ntlworld.com), Dec 07 2007
|
|
|
Search completed in 0.002 seconds
|
