A296442 Initial digit of n-th Mersenne number.
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, 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, 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
Offset: 1
Examples
The 4th Mersenne number is 127, so a(4) = 1.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
- Zhaodong Cai, Matthew Faust, A.J. Hildebrand, Junxian Li, Yuan Zhang, Leading Digits of Mersenne Numbers, arXiv:1712.04425 [math.NT], 2017.
Programs
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Maple
initialdig:= n -> floor(n/10^ilog10(n)): seq(initialdig(2^ithprime(i)-1),i=1..100); # Robert Israel, Dec 13 2017
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Mathematica
Array[First@ IntegerDigits[2^Prime[#] - 1] &, 105] (* Michael De Vlieger, Dec 13 2017 *)
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PARI
a(n) = digits(2^prime(n)-1)[1];