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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

Table of n, a(n) for n=0..25.

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 A211404

Adjacent sequences:  A222585 A222586 A222587 * A222589 A222590 A222591

KEYWORD

nonn,easy

AUTHOR

Walter Nissen, Feb 25 2013

STATUS

approved

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Last modified August 5 06:46 EDT 2020. Contains 336209 sequences. (Running on oeis4.)