A339023 - OEIS

%I #65 Feb 14 2021 13:17:01

%S 0,1,4,9,7,7,9,4,1,9,10,22,36,43,52,63,76,82,99,19,40,63,88,16,36,58,

%T 73,99,28,49,90,34,61,99,31,64,99,37,67,99,70,25,63,13,55,99,46,85,36,

%U 79,70,36,85,46,99,55,13,63,25,79,90,67,37,99,64,31,99,61

%N Replace each digit d in the decimal representation of n with the digital root of n*d.

%H Sebastian Karlsson, <a href="/A339023/b339023.txt">Table of n, a(n) for n = 0..10000</a>

%H Sebastian Karlsson, <a href="/A339023/a339023.pdf">The sequence generalized and plotted in arbitrary bases</a>

%F a(9*n + 1) = 9*n + 1.

%F a(10*n) = 10*a(n). - _Sebastian Karlsson_, Feb 14 2021

%e a(23) = 16 because 2*23 = 46 and 3*23 = 69 and the digital roots of 46 and 69 are 1 and 6.

%o (Python)

%o def digitalroot(n):

%o     return 0 if n == 0 else (n-1)%9 + 1

%o def a(n):

%o     return int(''.join([str(digitalroot(n*int(d))) for d in str(n)]))

%o for n in range(0, 68):

%o     print(a(n), end=', ')

%o (PARI) dr(n) = if(n, (n-1)%9+1); \\ A010888

%o 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

%Y Cf. A010888, A056992, A059729, A106649, A106746, A139337, A316347, A322131.

%K nonn,base,look

%O 0,3

%A _Sebastian Karlsson_, Jan 18 2021