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

1,1

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, ....

Links

Table of n, a(n) for n=1..50.

Example

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

Prog

(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

Crossrefs

Cf. A054723, A136030.

Sequence in context: A104066 A184394 A060160 * A158021 A239638 A050767

Adjacent sequences: A241970 A241971 A241972 * A241974 A241975 A241976

Keyword

nonn

Author

J. Lowell, May 03 2014

Extensions

More terms from Michel Marcus, May 14 2014

Status

approved