%I #13 Jul 20 2022 08:50:52

%S 1,1,8,1,2,3,1,2,7,1,2,4,6,10,12,22,28,1,2,3,4,10,30,1,2,3,6,12,14,21,

%T 27,30,56,92,1,25,154,1,2,3,4,8,10,19,24,28,30,80,93,1,6,7,17,81,123

%N Irregular triangle read by rows in which row n lists the possible periods for the iterations of the map sum of n-th powers of digits.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Digitaddition.html">Digitaddition</a>

%e Triangle begins:

%e 1;

%e 1, 8;

%e 1, 2, 3;

%e 1, 2, 7;

%e 1, 2, 4, 6, 10, 12, 22, 28;

%e 1, 2, 3, 4, 10, 30;

%e 1, 2, 3, 6, 12, 14, 21, 27, 30, 56, 92;

%e 1, 25, 154;

%e 1, 2, 3, 4, 8, 10, 19, 24, 28, 30, 80, 93;

%e 1, 6, 7, 17, 81, 123;

%e ...

%Y Periods of sum of m-th powers of digits iterated: A031176 (m=2), A031178 (m=3), A031182 (m=4), A031186 (m=5), A031195 (m=6), A031200 (m=7), A031211 (m=8), A031212 (m=9), A031213 (m=10).

%Y Sum of m-th powers of digits: A007953 (m=1), A003132 (m=2), A055012 (m=3), A055013 (m=4), A055014 (m=5), A055015 (m=6), A123253 (m=7), A210840 (m=8).

%K nonn,tabf,base,more

%O 1,3

%A _Mohammed Yaseen_, Jul 14 2022