A241973 Prime exponents of composite Mersenne numbers in the order of the magnitude of the smallest prime factor.

11, 23, 83, 37, 29, 131, 179, 191, 43, 73, 239, 251, 359, 419, 431, 443, 491, 659, 683, 233, 719, 743, 911, 1019, 1031, 1103, 47, 397, 1223, 79, 461, 1439, 1451, 1499, 1511, 1559, 1583, 557, 113, 577, 601, 1811, 1931, 2003, 2039, 2063, 761, 2339, 2351, 2399

Offset: 1

Author

J. Lowell, May 03 2014

Keywords

• nonn

Comments

Terms are the same as A054723, but in a different order.

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.

The corresponding smallest prime factors are: 23, 47, 167, 223, 233, 263, 359, 383, 431, 439, 479, 503, 719, 839, 863, 887, 983, ....

Examples

			83 comes before 37 because 167 (the smallest prime factor of 2^83-1) < 223 (the smallest prime factor of 2^37-1).
		

Crossrefs

Cf. A054723, A136030.

Programs

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

Extensions

More terms from Michel Marcus, May 14 2014