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%I #28 Nov 30 2019 17:22:53
%S 1,10,100,103,301,367,608,806,1000,1030,1826,2363,2618,2896,3010,3056,
%T 3640,4036,4498,4596,5294,5630,6080,6323,6703,6791,8060,8484,9167,
%U 9452,9628,9645,9844,10000,10003,10275,10300,10451,10979,11241,11540,12336,12770,12939,13623,13929,14015,14112,15104,15161,16151,16286,17027
%N Bihappy numbers: numbers that reach 1 under iteration of the sum-of-squares-of-two-digits map s_2.
%C If n has an even number of digits, say n = abcdef, the map is n -> s_2(n) := (ab)^2+(cd)^2+(ef)^2. If n has an odd number of digits, say n = abcde, the map is n -> s_2(n) = a^2+(bc)^2+(de)^2. The sequence {s_2(n), n >= 0} does not have its own entry in the OEIS because it begins {0, 1, ..., 9801, 1, 2, 5, ...} and agrees with A000290 for the first 100 terms. - _N. J. A. Sloane_, May 10 2015
%C This sequence is infinite because it contains several infinite subsequences (powers of 10, for example).
%H Pieter Post and Giovanni Resta, <a href="/A257795/b257795.txt">Table of n, a(n) for n = 1..10000</a> (first 244 terms from Pieter Post)
%F All 10^k are members of this sequence.
%F If n is a member each permutation of a set of pairs of digits gives another member.
%F Placing two zeros between the sets of two digits gives another member.
%F All other numbers have loops of lengths 1, 2, 4, 5, 6, 10, 14, 35 or 56.
%F The first number with a loop of length 2 is 51, which reaches the loop (5965, 7706) after 3 iterations.
%F The first number with a loop of length 4 is 342, loop of 5 is 57, loop of 6 is 389, loop of 10 is 21, loop of 14 is 28, loop of 35 is 2 and the first number with a loop of 56 is 5.
%F And there are some numbers which end up in a loop of length 1. The first such number is 1233 (= 12^2 + 33^2)
%F All numbers appear to end up in one of these loops.
%e 367 is in the sequence since 3^2+67^2 = 4498 => 44^2+98^2= 11540 => 1^2+15^2+40^2 = 1826 => 18^2+26^2 = 1000 => 10^2+0^2 = 100 =>1^2+0^2 = 1, so in 6 iterations 367 reaches 1.
%Y Cf. A007770, A055616, A000290.
%K nonn,base
%O 1,2
%A _Pieter Post_, May 09 2015
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