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

1,1

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.

Formula

a(n) = A000030(A001348(n)).

Example

The 4th Mersenne number is 127, so a(4) = 1.

Maple

initialdig:= n -> floor(n/10^ilog10(n)):
seq(initialdig(2^ithprime(i)-1), i=1..100); # Robert Israel, Dec 13 2017

Mathematica

Array[First@ IntegerDigits[2^Prime[#] - 1] &, 105] (* Michael De Vlieger, Dec 13 2017 *)

Prog

(PARI) a(n) = digits(2^prime(n)-1)[1];

Crossrefs

Cf. A000030, A001348.

A135613, for Mersenne primes, is a subsequence.

Sequence in context: A153027 A161127 A256978 * A021272 A135613 A019973

Adjacent sequences: A296439 A296440 A296441 * A296443 A296444 A296445

Keyword

nonn,base

Author

Michel Marcus, Dec 13 2017

Status

approved