This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341767 #23 Mar 23 2024 20:44:39
%S A341767 1,4,9,4,2,9,7,1,9,11,22,39,41,54,69,71,88,99,11,41,93,77,78,99,44,11,
%T A341767 99,11,48,91,14,87,99,17,88,99,11,84,99,41,45,99,71,11,99,11,72,99,41,
%U A341767 21,96,44,88,99,11,51,99,77,28,91,17,11,99,11,15,99,14
%N A341767 Replace each digit d in the decimal representation of n with the digital root of n^d.
%C A341767 If n == 1 (mod 9), then every digit will be replaced by "1". If n == 0 (mod 9), then all nonzero digits will be replaced by "9".
%C A341767 The corresponding n of values a(n)= 1, a(n)= 11, a(n)= 111,... creates a subsequence of A236653. - _Davide Rotondo_, Mar 04 2024
%H A341767 Sebastian Karlsson, <a href="/A341767/b341767.txt">Table of n, a(n) for n = 1..10000</a>
%H A341767 Sebastian Karlsson, <a href="/A341767/a341767.pdf">Generalized and plotted in arbitrary bases</a>
%F A341767 a(10*n) = 10*a(n) + 1.
%e A341767 a(26) = 11, since 26^2 = 676 and 26^6 = 308915776. 6 + 7 + 6 = 19, 1 + 9 = 10 and 1 + 0 = 1, so the digital root of 676 is 1. 3 + 0 + 8 + 9 + 1 + 5 + 7 + 7 + 6 = 46, 4 + 6 = 10 and 1 + 0 = 1, so the digital root of 308915776 is 1. Thus, for 26, both "2" and "6" will be replaced by "1".
%t A341767 a[n_] := FromDigits[Mod[n^IntegerDigits[n] - 1, 9] + 1]; Array[a, 100] (* _Amiram Eldar_, Feb 19 2021 *)
%o A341767 (Python)
%o A341767 def a(n):
%o A341767 return int(''.join(str((pow(n, int(d), 9)-1)%9 + 1) for d in str(n)))
%o A341767 (PARI) dr(n) = if(n, (n-1)%9+1); \\ A010888
%o A341767 a(n) = my(d=digits(n)); fromdigits(vector(#d, k, dr(n^d[k]))); \\ _Michel Marcus_, Feb 19 2021
%Y A341767 Cf. A010888, A106649, A139337, A322131, A339023.
%K A341767 nonn,base,look
%O A341767 1,2
%A A341767 _Sebastian Karlsson_, Feb 19 2021