A209385 Values of the first prefixing digits for Mersenne primes.

1, 1, 1, 4, 1, 10, 1, 36, 15, 58, 57, 55, 310, 177, 51, 2389, 973, 532, 1750, 63, 1032, 1240, 3757, 9994, 5854, 12870, 46147, 11923, 17113, 10296, 5977

Offset: 1

Author

Gilbert Mozzo, Mar 07 2012, Mar 18 2012

Keywords

• nonn
• base
• more

Examples

			For Mersenne 5, i.e., 8191, the first computed prefix is equal to 1 and gives 18191 which is also a prime, so a(5) = 1.
		

Links

• Henri Lifchitz and Renaud Lifchitz, PRP Top Records

Crossrefs

Cf. A000668 (Mersenne primes), A202136.

Programs

Mathematica

pfx[n_] := Module[{w = 10^(1+Floor[Log10[n]])}, k=n+w ; While[!PrimeQ[k], k+=w]; Floor[k/w]]; s={}; Do[m = 2^MersennePrimeExponent[n]-1; AppendTo[s, pfx[m]], {n, 1, 12}]; s (* Amiram Eldar, Nov 22 2018 based on Andrew Howroyd's pari code *)

PARI

pfx(n)={my(w=10^(1+logint(n,10)), k=n+w); while(!ispseudoprime(k), k+=w); k\w}
{ for(n=1, 500, my(p=1<Andrew Howroyd, Nov 17 2018