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A241973 Prime exponents of composite Mersenne numbers in the order of the magnitude of the smallest prime factor. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 01:12 EST 2022. Contains 358672 sequences. (Running on oeis4.)