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
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
Programs
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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<