This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A135928 #25 Feb 16 2025 08:33:07 %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, %T A135928 4,4,4,4,1,1,1,4,1,4,4,1,4,4 %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. %H A135928 Syed Asadulla, <a href="http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/digital-roots-of-mersenne-primes-and-even-perfect-numbers">Digital Roots of Mersenne Primes and Even Perfect Numbers</a>, The College Mathematics Journal, Vol. 15, No. 1. (1984), pp. 53-54. %H A135928 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>. %F A135928 a(n) = A010888(A000668(n)). %F A135928 For n > 2, a(n) = (A000043(n) mod 3)^2. - _Jens Kruse Andersen_, Jul 29 2014 %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, A010888, A135927. %K A135928 nonn,base,hard,more %O A135928 1,1 %A A135928 _Ant King_, Dec 07 2007 %E A135928 a(40)-a(43) (using A000043) from _Jens Kruse Andersen_, Jul 29 2014 %E A135928 a(44)-a(48) from mersenne.org added by _M Sayer_, Jan 05 2023