A222588 Composites of the form 2^n-1 or 2^n+1 that are non-multiples of 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

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 A338413

Adjacent sequences: A222585 A222586 A222587 * A222589 A222590 A222591

Keyword

nonn,easy

Author

Walter Nissen, Feb 25 2013

Status

approved