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Interstate 13 does not exist.
I-113 is an early California proposed number inconsistent with the interstate highway numbering convention.
I-113 (preliminary numbering) California
On April 1, 1958, California submitted to AASHO a numbering plan for its proposed interstates, including 3-digit spurs numbered in the low 100s and not associated with their parent interstates. Interstate 113 was the proposed number for what became the original alignment of I-680. 
This number was not compliant with AASHO's numbering convention and was rejected.
On August 7, 1958, California had bought in to the system and submitted I-680. This was approved, along with the rest of California's original interstate highway system, on Nov. 10, 1958. 
(Earlier in 1957, the state had submitted I-5 for this highway. Today's I-5 was to be called I-11 in that proposal.)