A106092 Even numbers and primes.

2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 28, 29, 30, 31, 32, 34, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 50, 52, 53, 54, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 70, 71, 72, 73, 74, 76, 78, 79, 80, 82, 83, 84, 86, 88, 89, 90, 92, 94, 96, 97

Offset

1,1

Links

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

Paulo A. Martin, The Galois group of x^n-x^(n-1)-...-x-1, Journal of Pure and Applied Algebra, Volume 190, Issues 1-3, 1 June 2004, Pages 213-223.

Formula

From Robert Israel, Jan 01 2019: (Start)

a(k-1+A000720(2*k)] = 2*k.

a((prime(k)-3)/2 + k] = prime(k) for k >= 2. (End)

Maple

map(op, [seq([2*k, `if`(isprime(2*k+1), 2*k+1, NULL)], k=1..100)]); # Robert Israel, Jan 01 2019

Mathematica

Union[Prime[Range[30]], Select[Range[113], EvenQ]]
DeleteCases[Range[2, 100], _?(OddQ[#]&&CompositeQ[#]&)] (* Harvey P. Dale, Dec 04 2021 *)

Prog

(PARI) isok(n) = isprime(n) || ((n%2) == 0); \\ Michel Marcus, Feb 24 2020
(Python)
from sympy import primepi
def A106092(n):
    m, k = n, 1+(n<<1)-primepi(n)-(n>>1)
    while m != k:
        m, k = k, 1+n+k-primepi(k)-(k>>1)
    return m # Chai Wah Wu, Jul 31 2024

Crossrefs

Cf. A000720.

Complement of A014076.

Sequence in context: A307646 A246786 A095949 * A210940 A257500 A121208

Adjacent sequences: A106089 A106090 A106091 * A106093 A106094 A106095

Keyword

nonn

Author

Zak Seidov, May 07 2005

Status

approved