A277801 a(n) = 2^(n - 1) - prime(n).

-1, -1, -1, 1, 5, 19, 47, 109, 233, 483, 993, 2011, 4055, 8149, 16337, 32715, 65477, 131011, 262077, 524217, 1048503, 2097073, 4194221, 8388519, 16777119, 33554331, 67108761, 134217621, 268435347, 536870799, 1073741697, 2147483517, 4294967159, 8589934453, 17179869035

Offset

1,5

Comments

Obviously all terms are odd. Only the first three terms are negative.

The law of small numbers says there are not enough small numbers for all the demands placed on them.

I think one of those demands is that there be a strong correlation between the powers of 2 and the prime numbers. The first four primes and the first four powers of 2 deliver. But then the powers of 2 rise, literally, exponentially, leaving the primes behind in the dust.

Links

Table of n, a(n) for n=1..35.

Formula

a(n) is approximately 2^(n - 1).

Mathematica

Table[2^(n - 1) - Prime[n], {n, 35}]

Crossrefs

Cf. A111209.

Sequence in context: A120289 A243895 A024191 * A328191 A100104 A015650

Adjacent sequences: A277798 A277799 A277800 * A277802 A277803 A277804

Keyword

sign,easy

Author

Alonso del Arte, Oct 31 2016

Status

approved