|
%I #30 May 21 2014 00:05:58
%S 11,23,83,37,29,131,179,191,43,73,239,251,359,419,431,443,491,659,683,
%T 233,719,743,911,1019,1031,1103,47,397,1223,79,461,1439,1451,1499,
%U 1511,1559,1583,557,113,577,601,1811,1931,2003,2039,2063,761,2339,2351,2399
%N Prime exponents of composite Mersenne numbers in the order of the magnitude of the smallest prime factor.
%C Terms are the same as A054723, but in a different order.
%C If p is a prime and 2^p-1 is composite, each prime factor of 2^p-1 will be of the form kp+1 for some integer k. Thus, the smallest prime factor of 2^p-1 cannot be smaller than p.
%C The corresponding smallest prime factors are: 23, 47, 167, 223, 233, 263, 359, 383, 431, 439, 479, 503, 719, 839, 863, 887, 983, ....
%e 83 comes before 37 because 167 (the smallest prime factor of 2^83-1) < 223 (the smallest prime factor of 2^37-1).
%o (PARI) lista() = {vi = readvec("b054723.txt"); vm = vector(#vi, i, 2^vi[i]-1); p = 2; nbf = 0; while ( nbf != #vm, i = 1; while (!(i>#vm) && (!vm[i] || (vm[i] % p)), i++); if (i <= #vm, print1(vi[i], ", "); vm[i] = 0; nbf ++;); p = nextprime(p+1););} \\ _Michel Marcus_, May 14 2014
%Y Cf. A054723, A136030.
%K nonn
%O 1,1
%A _J. Lowell_, May 03 2014
%E More terms from _Michel Marcus_, May 14 2014
|
