A283623 a(n) = prime(n) + (1 + prime(1 + n))/2.

4, 6, 9, 13, 18, 22, 27, 31, 38, 45, 50, 58, 63, 67, 74, 83, 90, 95, 103, 108, 113, 121, 128, 138, 148, 153, 157, 162, 166, 177, 193, 200, 207, 214, 225, 230, 239, 247, 254, 263, 270, 277, 288, 292, 297, 305, 323, 337, 342, 346, 353, 360, 367

Offset

1,1

Comments

Primes occur at n = {4, 8, 14, 16, 19, 21, 27, 31, 37, 40, 42, 48, 51, 53, ...}: {13, 31, 67, 83, 103, 113, 157, 193, 239, 263, 277, 337, 353, 367, 389, 463, 563, 571, ...}.

Squares occur at n = {1, 3, 22, 35, 109, 136, 908, 936, ...}: {4, 9, 121, 225, 900, 1156, 10609, 11025, ...}.

Semiprimes: 4, 6, 9, 22, 38, 58, 74, 95, 121, 166, ...

Other interesting terms(?).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1) = 2 + (1 + 3)/2 = 4,
a(2) = 3 + (1 + 5)/2 = 6,
a(3) = 5 + (1 + 7)/2 = 9.

Maple

Primes:= [seq(ithprime(i), i=1..101)]:
map(`+`, Primes[1..-2] + Primes[2..-1]/2, 1/2); # Robert Israel, Jun 20 2019

Mathematica

Table[Prime[k] + (1 + Prime[1 + k])/2, {k, 120}]

Prog

(PARI) for(n=1, 53, print1(prime(n) + (1 + prime(1 + n))/2, ", "))  \\ Indranil Ghosh, Mar 12 2017

Crossrefs

Cf. A000040 (primes).

Sequence in context: A085802 A084916 A187910 * A020747 A010737 A048625

Adjacent sequences: A283620 A283621 A283622 * A283624 A283625 A283626

Keyword

nonn

Author

Zak Seidov, Mar 12 2017

Status

approved