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Decimal numbers n such that after possibly prefixing a leading 0 to n, the resulting number n' can be broken into 2 strings of the same length, n' = xy, such that x^2+y^2 = n.
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%I #14 May 11 2015 12:55:01

%S 1,1233,8833,10100,990100,5882353,94122353,1765038125,2584043776,

%T 7416043776,8235038125,116788321168,123288328768,876712328768,

%U 883212321168,7681802663025,8896802846976,13793103448276

%N Decimal numbers n such that after possibly prefixing a leading 0 to n, the resulting number n' can be broken into 2 strings of the same length, n' = xy, such that x^2+y^2 = n.

%C Define a map s_2(n) as follows. 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. There are exactly three numbers such that s_2(n) = n, namely 1, 1233, 8833. - _N. J. A. Sloane_ and _Pieter Post_, May 11 2015

%H Colin Barker, <a href="/A101311/a101311.html">An extended list of terms</a>

%e 1233 is in the sequence because 12^2+33^2 = 1233.

%e 5882353 is in the sequence because 588^2+2353^2 = 5882353.

%Y See A064942 for another version.

%K nonn,base

%O 1,2

%A _Colin Barker_, Jul 31 2007, Aug 01 2007