

A260868


Numbers for which the least k > 1 which divides n + 2^k  2 is different from the smallest prime factor of n.


1



89, 173, 179, 229, 269, 439, 499, 509, 523, 557, 577, 599, 619, 677, 719, 769, 797, 839, 859, 929, 1009, 1013, 1031, 1049, 1061, 1069, 1109, 1129, 1217, 1223, 1237, 1259, 1279, 1291, 1303, 1319, 1447, 1471, 1483, 1489, 1499, 1523, 1559, 1579, 1601, 1609, 1667, 1699, 1709, 1721, 1783, 1789, 1811, 1879, 1889, 1931, 1933
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OFFSET

1,1


COMMENTS

Somewhat astonishingly, n = 89 is the only number below 173 for which the least prime factor is different from the least k > 1 which divides n + 2^k  2. For larger n, this property becomes more frequent.
The first composite number in this sequence is a(105) = 3239.


LINKS



PROG

(PARI) my(aa(n)=for(k=2, 9e9, Mod(2, k)^k+n2return(k))); for(n=2, 1e5, aa(n)!=factor(n)[1, 1]&&print1(n", "))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



