A101311 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.

1, 1233, 8833, 10100, 990100, 5882353, 94122353, 1765038125, 2584043776, 7416043776, 8235038125, 116788321168, 123288328768, 876712328768, 883212321168, 7681802663025, 8896802846976, 13793103448276

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..18.

Colin Barker, An extended list of terms

Example

1233 is in the sequence because 12^2+33^2 = 1233.
5882353 is in the sequence because 588^2+2353^2 = 5882353.

Crossrefs

See A064942 for another version.

Sequence in context: A270540 A206272 A064942 * A055616 A104971 A193492

Adjacent sequences: A101308 A101309 A101310 * A101312 A101313 A101314

Keyword

nonn,base

Author

Colin Barker, Jul 31 2007, Aug 01 2007

Status

approved