A292384 a(1) = 1; for n > 1, a(n) = 4*a(A252463(n)) + (n mod 4).

1, 6, 27, 24, 109, 110, 439, 96, 97, 438, 1759, 440, 7037, 1758, 443, 384, 28149, 390, 112599, 1752, 1753, 7038, 450399, 1760, 389, 28150, 387, 7032, 1801597, 1774, 7206391, 1536, 7033, 112598, 1775, 1560, 28825565, 450398, 28155, 7008, 115302261, 7014, 461209047, 28152, 1761, 1801598, 1844836191, 7040, 1557, 1558, 112603, 112600

Offset: 1

Author

Antti Karttunen, Sep 15 2017

Keywords

• nonn
• base

Comments

a(n) encodes in its base-4 representation the succession of modulo 4 residues obtained when map x -> A252463(x), starting from x=n, is iterated down to the eventual 1.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024

Crossrefs

Cf. A010873, A252463, A292380, A292381, A292382, A292383.

Cf. also A292243.

Programs

Python

from sympy.core.cache import cacheit
from sympy import factorint, prevprime, prod
def a064989(n):
    f = factorint(n)
    return 1 if n == 1 else prod(prevprime(i)**f[i] for i in f if i != 2)
def a252463(n): return 1 if n==1 else n//2 if n%2==0 else a064989(n)
@cacheit
def a(n): return 1 if n==1 else 4*a(a252463(n)) + n%4
print([a(n) for n in range(1, 51)]) # Indranil Ghosh, Sep 21 2017

Formula

a(1) = 1; for n > 1, a(n) = 4*a(A252463(n)) + A010873(n).