A135613 Initial digit of Mersenne primes A000668.

3, 7, 3, 1, 8, 1, 5, 2, 2, 6, 1, 1, 6, 5, 1, 1, 4, 2, 1, 2, 4, 3, 2, 4, 4, 4, 8, 5, 5, 5, 7, 1, 1, 4, 8, 6, 1, 4, 9, 1, 2, 1, 3, 1, 2, 1, 3, 5

Offset: 1

Author

Omar E. Pol, Mar 01 2008

Keywords

• nonn
• base
• more

Examples

			a(4) = 1 because the 4th Mersenne prime A000668(4) is 127 and the initial digit of 127 is 1.
		

Links

• Landon Curt Noll, Mersenne Prime Digits.

Crossrefs

Cf. A000030, A000668, A077648, A080172.

Programs

Mathematica

lst = {* the list of terms in A000043 *}; f[n_] := Block[{pn = 2^n - 1}, Quotient[pn, 10^Floor[ Log[10, pn]] ]]; f@# & /@ lst (* Robert G. Wilson v, Apr 01 2008 *)
IntegerDigits[#][[1]]&/@(2^#-1&/@MersennePrimeExponent[Range[47]]) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 04 2019 *)

Formula

a(n) = A000030(A000668(n)). - Omar E. Pol, Jul 04 2019

Extensions

More terms from Robert G. Wilson v, Apr 01 2008

a(40)-a(44) from David Radcliffe, Jan 21 2016

a(45)-a(47) from Ivan Panchenko, Apr 11 2018

a(48) from Amiram Eldar, Oct 16 2024