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Numbers that eventually reach 1 under "x -> sum of 4th power of digits of x".
2

%I #8 Mar 14 2015 10:11:58

%S 1,10,100,1000,10000,11123,11132,11213,11231,11312,11321,12113,12131,

%T 12311,13112,13121,13211,21113,21131,21311,23111,31112,31121,31211,

%U 32111,44688,44868,44886,46488,46848,46884,48468,48486,48648,48684,48846,48864,64488

%N Numbers that eventually reach 1 under "x -> sum of 4th power of digits of x".

%e 11123 is in the sequence because 1^4 +1^4+1^4+2^4+3^4 = 100 and 1^4 + 0^4 + 0^4 = 1.

%e 2 is not in the sequence because 2 --> 16 --> 1297 -->8979 -->19619 -->14420 -->529 -->7202 -->2433 -->434 -->593 -->7267 -->6114 -->1554 -->1507 -->3027 -->2498 -->10929 -->13139 -->6725 -->4338 -->4514 -->1138 -->4179 -->9219 -->13139 which repeats with period 7, so never reaches 1.

%t Select[Range[50000], FixedPoint[Total[IntegerDigits[#]^4]&, #, 10]==1&]

%Y Cf. A007770, A035504.

%K nonn,base

%O 1,2

%A _Michel Lagneau_, Nov 12 2012