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

Author

Alonso del Arte, Oct 31 2016

Keywords

• sign
• easy

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.

Crossrefs

Cf. A111209.

Programs

Mathematica

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

Formula

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