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

%I A339023 #65 Feb 14 2021 13:17:01
%S A339023 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 A339023 73,99,28,49,90,34,61,99,31,64,99,37,67,99,70,25,63,13,55,99,46,85,36,
%U A339023 79,70,36,85,46,99,55,13,63,25,79,90,67,37,99,64,31,99,61
%N A339023 Replace each digit d in the decimal representation of n with the digital root of n*d.
%H A339023 Sebastian Karlsson, <a href="/A339023/b339023.txt">Table of n, a(n) for n = 0..10000</a>
%H A339023 Sebastian Karlsson, <a href="/A339023/a339023.pdf">The sequence generalized and plotted in arbitrary bases</a>
%F A339023 a(9*n + 1) = 9*n + 1.
%F A339023 a(10*n) = 10*a(n). - _Sebastian Karlsson_, Feb 14 2021
%e A339023 a(23) = 16 because 2*23 = 46 and 3*23 = 69 and the digital roots of 46 and 69 are 1 and 6.
%o A339023 (Python)
%o A339023 def digitalroot(n):
%o A339023     return 0 if n == 0 else (n-1)%9 + 1
%o A339023 def a(n):
%o A339023     return int(''.join([str(digitalroot(n*int(d))) for d in str(n)]))
%o A339023 for n in range(0, 68):
%o A339023     print(a(n), end=', ')
%o A339023 (PARI) dr(n) = if(n, (n-1)%9+1); \\ A010888
%o A339023 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 A339023 Cf. A010888, A056992, A059729, A106649, A106746, A139337, A316347, A322131.
%K A339023 nonn,base,look
%O A339023 0,3
%A A339023 _Sebastian Karlsson_, Jan 18 2021