cp's OEIS Frontend

A352751 Modified Sisyphus function of order 4: a(n) is the concatenation of (number of digits of n)(number digits of n congruent to 0 modulo 4)(number of digits of n congruent to 1 modulo 4)(number of digits of n congruent to 2 modulo 4)(number of digits of n congruent to 3 modulo 4).

%I A352751 #8 May 13 2022 10:12:22
%S A352751 11000,10100,10010,10001,11000,10100,10010,10001,11000,10100,21100,
%T A352751 20200,20110,20101,21100,20200,20110,20101,21100,20200,21010,20110,
%U A352751 20020,20011,21010,20110,20020,20011,21010,20110,21001,20101,20011,20002,21001,20101,20011,20002,21001,20101,22000,21100,21010
%N A352751 Modified Sisyphus function of order 4: a(n) is the concatenation of (number of digits of n)(number digits of n congruent to 0 modulo 4)(number of digits of n congruent to 1 modulo 4)(number of digits of n congruent to 2 modulo 4)(number of digits of n congruent to 3 modulo 4).
%C A352751 If we start with n and repeatedly apply the map i -> a(i), we eventually get one of three cycles:  {51220}, {50410, 52111, 53200}, or {51301}
%D A352751 M. E. Coppenbarger, Iterations of a modified Sisyphus function, Fib. Q., 56 (No. 2, 2018), 130-141.
%e A352751 11 has two digits, both congruent to 1 modulo 4, so a(11) = 20200.
%e A352751 a(20) = 21010.
%e A352751 a(30) = 21001.
%e A352751 a(1111123567) = 100622.
%o A352751 (Python)
%o A352751 def a(n, order=4):
%o A352751     d, m = list(map(int, str(n))), [0]*order
%o A352751     for di in d: m[di%order] += 1
%o A352751     return int(str(len(d)) + "".join(map(str, m)))
%o A352751 print([a(n) for n in range(37)]) # _Michael S. Branicky_, Apr 01 2022
%Y A352751 Cf. A073053 (Sisyphus), A171797, A171798, A171813, A055642, A196563, A196564, A308002, A350709.
%K A352751 nonn,base,easy
%O A352751 0,1
%A A352751 _Matthew E. Coppenbarger_, Apr 01 2022