A339023 Replace each digit d in the decimal representation of n with the digital root of n*d.

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, 73, 99, 28, 49, 90, 34, 61, 99, 31, 64, 99, 37, 67, 99, 70, 25, 63, 13, 55, 99, 46, 85, 36, 79, 70, 36, 85, 46, 99, 55, 13, 63, 25, 79, 90, 67, 37, 99, 64, 31, 99, 61

Offset: 0

Author

Sebastian Karlsson, Jan 18 2021

Keywords

• nonn
• base
• look

Examples

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

Links

• Sebastian Karlsson, Table of n, a(n) for n = 0..10000
• Sebastian Karlsson, The sequence generalized and plotted in arbitrary bases

Crossrefs

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

Programs

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

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=', ')

Formula

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

a(10*n) = 10*a(n). - Sebastian Karlsson, Feb 14 2021