A111209 -id:A111209 - cp's OEIS frontend

A265160 a(n) = 2^n + prime(n).

4, 7, 13, 23, 43, 77, 145, 275, 535, 1053, 2079, 4133, 8233, 16427, 32815, 65589, 131131, 262205, 524355, 1048647, 2097225, 4194383, 8388691, 16777305, 33554529, 67108965, 134217831, 268435563, 536871021, 1073741937, 2147483775, 4294967427, 8589934729

Offset: 1

Vincenzo Librandi, Dec 03 2015

a(n) is odd for n>1. The first few primes in this sequence are 7, 13, 23, 43, 4133, 8233, 16427, 8388691, ... . - Wesley Ivan Hurt, Dec 05 2015

Cf. A000040, A000079, A100484, A111209.

Magma
```
[NthPrime(n) + 2^n: n in [1..40]];
```

A265160:=n->2^n + ithprime(n): seq(A265160(n), n=1..40); # Wesley Ivan Hurt, Dec 05 2015

Mathematica
```
Table[2^n + Prime[n], {n, 40}]
```

a(n) = 2^n + prime(n); \\ Altug Alkan, Dec 03 2015

From Wesley Ivan Hurt, Dec 05 2015: (Start)
a(n) = A000079(n) + A000040(n), for n>0.
a(n) = A100484(n) + A111209(n). (End)

A111210 Primes of the form (2^k - prime(k))/3.

Original entry on oeis.org

3, 7, 17, 37, 79, 163, 183251937907, 96076792050570491, 27043212804868893898596335047829, 1772303994379887830538409413707125877, 510831846955296286119449009050103061206246374061200369

Offset: 1

Roger L. Bagula, Oct 25 2005

nonn

Corresponding k's are 4, 5, 6, 7, 8, 9, 39, 58, 106, 122, 180, 309, 357, 696, ... - Michel Marcus, Jul 04 2021

Cf. A111209.

a = Flatten[Table[If[PrimeQ[(2^n - Prime[n])/3] == True, (2^n - Prime[n])/3, {}], {n, 1, 100}]]
Table[ If[PrimeQ[(2^n - Prime[n])/3], (2^n - Prime[n])/3, {}], {n, 1, 200}]//Flatten (* Robert G. Wilson v, Oct 31 2005 *)

a(9)-a(11) from Robert G. Wilson v, Oct 31 2005

Edited by N. J. A. Sloane, Nov 19 2005

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

Original entry on oeis.org

-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

Alonso del Arte, Oct 31 2016

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.

Cf. A111209.

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

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

cp's OEIS Frontend

A265160 a(n) = 2^n + prime(n).

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A111210 Primes of the form (2^k - prime(k))/3.

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

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