A256420 a(n) = 2n unless n is prime, in which case a(n) = first term not yet present in the sequence.

2, 1, 3, 8, 4, 12, 5, 16, 18, 20, 6, 24, 7, 28, 30, 32, 9, 36, 10, 40, 42, 44, 11, 48, 50, 52, 54, 56, 13, 60, 14, 64, 66, 68, 70, 72, 15, 76, 78, 80, 17, 84, 19, 88, 90, 92, 21, 96, 98, 100, 102, 104, 22, 108, 110, 112, 114, 116, 23, 120

Offset: 1

Author

N. J. A. Sloane, Apr 07 2015

Keywords

• nonn

Comments

This is a permutation of the positive integers: twice nonprimes (A139270), interspersed with (odd numbers and twice primes, A256421).

References

• John Mason, Email message, Apr 07 2015

Links

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

Crossrefs

Cf. A139270, A256421.

Programs

Maple

N:= 100:
S:= {$1..N}:
R:= NULL;
for n from 1 do
  if isprime(n) then if S = {} then break else t:= min(S) fi else t:= 2*n fi;
  R:= R, t;
  S:= S minus {t}
od:
R;

Python

from sympy import primepi, isprime
def A256420(n):
    r = int(primepi(n))
    def iterfun(f,n=0):
        m, k = n, f(n)
        while m != k: m, k = k, f(k)
        return m
    def f(x): return int(r+(m:=x>>1)-primepi(m))
    return iterfun(f,r) if isprime(n) else n<<1 # Chai Wah Wu, Oct 15 2024