OFFSET
0,3
LINKS
Sebastian Karlsson, Table of n, a(n) for n = 0..10000
Sebastian Karlsson, The sequence generalized and plotted in arbitrary bases
FORMULA
a(9*n + 1) = 9*n + 1.
a(10*n) = 10*a(n). - Sebastian Karlsson, Feb 14 2021
EXAMPLE
a(23) = 16 because 2*23 = 46 and 3*23 = 69 and the digital roots of 46 and 69 are 1 and 6.
PROG
(Python)
def digitalroot(n):
return 0 if n == 0 else (n-1)%9 + 1
def a(n):
return int(''.join([str(digitalroot(n*int(d))) for d in str(n)]))
for n in range(0, 68):
print(a(n), end=', ')
(PARI) dr(n) = if(n, (n-1)%9+1); \\ A010888
a(n) = if (n==0, return(0)); my(d=digits(n), s=""); for (k=1, #d, s=concat(s, dr(n*d[k]))); eval(s); \\ Michel Marcus, Jan 18 2021
CROSSREFS
KEYWORD
AUTHOR
Sebastian Karlsson, Jan 18 2021
STATUS
approved