

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

Table of n, a(n) for n=0..25.
Wikipedia, Mersenne number
Wikipedia, Fermat number
George Woltman, GIMPS


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

Subsequence of both A014551 and A166977.
Sequence in context: A020292 A251158 A251151 * A286612 A276963 A211404
Adjacent sequences: A222585 A222586 A222587 * A222589 A222590 A222591


KEYWORD

nonn,easy


AUTHOR

Walter Nissen, Feb 25 2013


STATUS

approved



