Consecutive number sequences are sequences constructed by concatenating numbers of a given type. Many of these sequences were considered by Smarandache and so are sometimes known as Smarandache sequences. The most obvious consecutive number sequence is the sequence of the first n positive integers joined left-to-right, namely 1, 12, 123, 1234, ... (OEIS A007908; Smarandache 1993, Dumitrescu and Seleacu 1994, sequence 1; Mudge 1995; Stephan 1998; Wolfram 2002, p. 913). In this work, members of this sequence will be termed Smarandache numbers and the nth such number written Sm(n). No Smarandache primes Sm(n) exist for n<=344869 (Great Smarandache PRPrime search; Dec. 5, 2016).

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