cp's OEIS Frontend

A341817 If a(n) is odd, add to a(n) its odd digits and iterate; if a(n) is even, add to a(n) its even digits and iterate; if an iteration reproduces a term already in the sequence, don't do this iteration and extend the sequence with the smallest integer not yet present in the sequence.

%I A341817 #8 Feb 24 2021 12:08:15
%S A341817 1,2,4,8,16,22,26,34,38,46,56,62,70,3,6,12,14,18,5,10,7,9,11,13,17,25,
%T A341817 30,15,21,19,29,20,23,24,27,28,31,35,43,32,33,39,51,57,69,78,86,100,
%U A341817 36,42,48,60,66,37,47,54,58,40,44,52,41,45,50,49,53,61,55,65,59,73,83,63,64,74,67,68,82,92
%N A341817 If a(n) is odd, add to a(n) its odd digits and iterate; if a(n) is even, add to a(n) its even digits and iterate; if an iteration reproduces a term already in the sequence, don't do this iteration and extend the sequence with the smallest integer not yet present in the sequence.
%C A341817 This sequence is, by definition, a permutation of the positive integers.
%H A341817 Carole Dubois, <a href="/A341817/b341817.txt">Table of n, a(n) for n = 1..5000</a>
%e A341817 a(1) = 1, odd, a(2) is thus 1 + 1 = 2;
%e A341817 a(2) = 2, even, thus a(3) = 2 + 2 = 4;
%e A341817 a(3) = 4, even, thus a(4) = 4 + 4 = 8;
%e A341817 a(4) = 8, even, thus a(5) = 8 + 8 = 16;
%e A341817 a(5) = 16, even, thus a(6) = 16 + 6 = 22;
%e A341817 a(6) = 22, even, thus a(7) = 22 + 2 + 2 = 26;
%e A341817 ...
%e A341817 a(13) = 70, even, thus a(14) = 70 + 0 = 70 (already in the sequence, thus a(14) = 3 instead, the smallest integer not yet present in the sequence);
%e A341817 a(14) = 3, odd, thus a(15) = 3 + 3 = 6;
%e A341817 a(15)  = 6, even, thus a(16) = 6 + 6 = 12;
%e A341817 a(16) = 12, even, thus a(17) =  12 + 2 = 14;
%e A341817 a(17) = 14, even, thus a(18) = 14 + 4 = 18;
%e A341817 a(18) =  18, even, thus a(19) = 18 + 6 = 26 (already in the sequence, thus a(19) = 5 instead, the smallest integer not yet present in the sequence);
%e A341817 a(19) = 5, odd, thus a(20) = 5 + 5 = 10; etc.
%Y A341817 Cf. A004207 (sum of digits of all previous terms).
%K A341817 base,nonn
%O A341817 1,2
%A A341817 _Eric Angelini_ and _Carole Dubois_, Feb 20 2021