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 A135928 Digital roots of the Mersenne primes. 2
 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, 1, 1, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. LINKS Syed Asadulla, Digital Roots of Mersenne Primes and Even Perfect Numbers, The College Mathematics Journal, Vol. 15, No. 1. (1984), pp. 53-54. Eric Weisstein's World of Mathematics, Digital Root. FORMULA a(n) = A010888(A000668(n)). For n > 2, a(n) = (A000043(n) mod 3)^2. - Jens Kruse Andersen, Jul 29 2014 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, A010888, A135927. Sequence in context: A200129 A181912 A108297 * A011444 A272004 A010471 Adjacent sequences:  A135925 A135926 A135927 * A135929 A135930 A135931 KEYWORD hard,nonn,base AUTHOR Ant King, Dec 07 2007 EXTENSIONS a(40)-a(43) (using A000043) from Jens Kruse Andersen, Jul 29 2014 STATUS approved

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Last modified March 28 20:01 EDT 2020. Contains 333103 sequences. (Running on oeis4.)