Hi Steve, Trying to find anyone after the 1930 Census is a challenge.
I found that an Arthur Martin and family in 1930 were living in San Diego, San Diego Co., CA. ARthur E. Martin, b. IN, 27 yrs old, marr @ 24, sailor U. S. Navy. Madeline E., wife, b. CA, 25, marr @ 22. Elizabeth A., b. CA, 6/12ths. John H. Alexander, lodger.
An ARthur Martin b. 22 Nov 1902, Last Residence=Diamond Springs, El Dorado Co., CA died Oct. 1982. His soc. Sec. # was assigned in California before 1951. Source: Social Security Death Index, Ancestry.