

A222588


Composites of the form 2^n1 or 2^n+1 that are nonmultiples of 3.


3



65, 511, 1025, 2047, 4097, 16385, 32767, 262145, 1048577, 2097151, 4194305, 8388607, 16777217, 33554431, 67108865, 134217727, 268435457, 536870911, 1073741825, 4294967297, 8589934591, 17179869185, 34359738367, 68719476737, 137438953471, 274877906945
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OFFSET

0,1


COMMENTS

Half the numbers of the proper form are divisible by 3 and thus excluded.
For 2^n1, n must be odd to be in this sequence.
For 2^n+1, n must be even to be in this sequence.


REFERENCES

Oystein Ore, Number Theory and Its History, McGrawHill, 1948, reprinted 1988, section 47, pp 6975.


LINKS



EXAMPLE

31 = 2^51 is prime and thus not a member of the sequence.
65 = 2^6+1 has 2 proper divisors, 5 and 13, thus is a(0) in the sequence.


MATHEMATICA

t = 2^Range[50]; u = Union[t  1, t + 1]; Select[u, # > 1 && Mod[#, 3] != 0 && ! PrimeQ[#] &] (* T. D. Noe, Feb 26 2013 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



