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A222588 Composites of the form 2^n-1 or 2^n+1 that are non-multiples 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^n-1, 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, McGraw-Hill, 1948, reprinted 1988, section 4-7, pp 69-75.
LINKS
Wikipedia, Mersenne number
Wikipedia, Fermat number
George Woltman, GIMPS
EXAMPLE
31 = 2^5-1 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 A338413
KEYWORD
nonn,easy
AUTHOR
Walter Nissen, Feb 25 2013
STATUS
approved

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Last modified May 23 21:14 EDT 2024. Contains 372765 sequences. (Running on oeis4.)