A347859 a(n) = n/2 if n/2 is a prime, else 3(n-1)/2 if (n-1)/2 is prime, else n.

0, 1, 2, 3, 2, 6, 3, 9, 8, 9, 5, 15, 12, 13, 7, 21, 16, 17, 18, 19, 20, 21, 11, 33, 24, 25, 13, 39, 28, 29, 30, 31, 32, 33, 17, 51, 36, 37, 19, 57, 40, 41, 42, 43, 44, 45, 23, 69, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 29, 87, 60, 61, 31, 93, 64, 65, 66, 67, 68, 69, 70

Offset

0,3

Comments

Inspired by the "EKG permutation" A064413 which has a quite similar graph (a main ray with slope 1 and two secondary rays with slope 1/2 and 3/2) but probably not many other common properties.

Links

Table of n, a(n) for n=0..70.

Prog

(PARI) apply( {a(n)=if(!isprime(n\2), n, n%2, n\2*3, n\2)}, [0..88])
(Python)
from sympy import isprime
def a(n):
    if n%2 == 0 and isprime(n//2): return n//2
    if (n-1)%2 == 0 and isprime((n-1)//2): return 3*(n-1)//2
    return n
print([a(n) for n in range(71)]) # Michael S. Branicky, Feb 21 2022

Crossrefs

Cf. A064413 (EKG permutation), A100484 (twice the primes = even semiprimes).

Sequence in context: A329282 A197289 A161888 * A157224 A097914 A286633

Adjacent sequences: A347856 A347857 A347858 * A347860 A347861 A347862

Keyword

nonn,easy

Author

M. F. Hasler, Feb 14 2022

Status

approved