Search: id:A135928
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%I A135928
%S A135928 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,
%T A135928 4,4,4,1
%N A135928 Digital roots of the Mersenne primes.
%C A135928 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.
%D A135928 Asadulla, Syed; Digital Roots of Mersenne Primes and Even Perfect Numbers, 
               The College Mathematics Journal, Vol. 15, No. 1. (1984), pp. 53-54.
%H A135928 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DigitalRoot.html">Digital Root</a>.
%F A135928 a(n)=digital root of A000668(n).
%e A135928 The fourth Mersenne prime is 127, which has a digital root of 1. Hence 
               a(4)=1.
%t A135928 DigitalRoot[n_]:=FixedPoint[Plus@@IntegerDigits[ # ]&,n];data1=Select[Range[4500],
               PrimeQ[2^#-1] &];data2=2^#-1 &/@data1;DigitalRoot/@data2
%Y A135928 Cf. A000668, A000043, A003010, A001566, A135927.
%Y A135928 Sequence in context: A050393 A110778 A108297 this_sequence A011444 A010471 
               A077226
%Y A135928 Adjacent sequences: A135925 A135926 A135927 this_sequence A135929 A135930 
               A135931
%K A135928 hard,nonn,base
%O A135928 1,1
%A A135928 Ant King (mathstutoring(AT)ntlworld.com), Dec 07 2007

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