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A296442 Initial digit of n-th Mersenne number.

%I A296442 #14 Dec 14 2017 03:44:35
%S A296442 3,7,3,1,2,8,1,5,8,5,2,1,2,8,1,9,5,2,1,2,9,6,9,6,1,2,1,1,6,1,1,2,1,6,
%T A296442 7,2,1,1,1,1,7,3,3,1,2,8,3,1,2,8,1,8,3,3,2,1,9,3,2,3,1,1,2,4,1,2,4,2,
%U A296442 2,1,1,1,3,1,1,1,1,3,5,1,1,5,5,2,1,2,1,3,5,2,3,1,3,6,1,2,1,6,2,7
%N A296442 Initial digit of n-th Mersenne number.
%H A296442 Robert Israel, <a href="/A296442/b296442.txt">Table of n, a(n) for n = 1..10000</a>
%H A296442 Zhaodong Cai, Matthew Faust, A.J. Hildebrand, Junxian Li, Yuan Zhang, <a href="https://arxiv.org/abs/1712.04425">Leading Digits of Mersenne Numbers</a>, arXiv:1712.04425 [math.NT], 2017.
%F A296442 a(n) = A000030(A001348(n)).
%e A296442 The 4th Mersenne number is 127, so a(4) = 1.
%p A296442 initialdig:= n -> floor(n/10^ilog10(n)):
%p A296442 seq(initialdig(2^ithprime(i)-1),i=1..100); # _Robert Israel_, Dec 13 2017
%t A296442 Array[First@ IntegerDigits[2^Prime[#] - 1] &, 105] (* _Michael De Vlieger_, Dec 13 2017 *)
%o A296442 (PARI) a(n) = digits(2^prime(n)-1)[1];
%Y A296442 Cf. A000030, A001348.
%Y A296442 A135613, for Mersenne primes, is a subsequence.
%K A296442 nonn,base
%O A296442 1,1
%A A296442 _Michel Marcus_, Dec 13 2017