On an unsolved question about the Smarandache Square-Partial-Digital Subsequence

Felice Russo 1vIicrolZ Technology ltal)/ Avezzano (Aq) ItaZv In this not~ we r~port the solution of an unsolved qu~stion on Smarandache Squar~-Partial-Digital Subsequ~nce. We have found it by ~xtesi\'~ computer search. Some n~w questions about palindromic numb~rs and prime numbers in SSPDS are posed too. Introduction The Smarandache Square-Partial-Digital Subsequence (SSPDS) is the sequenc~ of square int~g~rs which admits a partition for \vhich each s~gment is a square integer [1].[2].[3). The tirst tenns of the s~qu~nce follow: 49,144.169.361,441,1225.1369.1444,1681,1936. 3249,4225.4900,11449,12544.14641,15625,16900 ... or 7.12.13.19.21,35,37,38.41. 44.57,65,70,107.112.121,125,130,190.191,204,205, 209. 212. 223, 253 ... reporting th~ value o1'n/\2 that can be partitioned into t\vo or more numbers that are also squares (A048653) [5]. Differently from the sequences reported in [I], [2] and [3] the proposed ones don't contain tenns that admit 0 as partition. In fact as reported in [4] we don't consider the number zero a perfect square. So, for example. the term 256036 and the term 506 respectively. are not reported in the above sequences because the partion 2S6iOi36 contains the number zero. L. Widmer explored some properties of S SPDS's and posed the following question [2]: Is there a sequence of three or more consecutive integers whose squares are in SPDS') Tnis note gives an anS\Ver to this question. Results A computer code has been \vritten in l.Jbasic Rev. 9. After about three week of work only a solution for three consecutive integers has been found. Those consecutive integers are: 12225,12226.12227.