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

Author

Walter Nissen, Feb 25 2013

Keywords

• nonn
• easy

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.

Examples

			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.
		

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

Crossrefs

Subsequence of both A014551 and A166977.

Programs

Mathematica

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