Actually
My Super Set does Span the Sub Set.
What makes Sequences difficult is that many times there is more that one unique Solution Set.
My Super Set is based on Right most integer value for the sub set which follows the form:
1, 4, 7, 1, 5, 8, 1, 4, 7, 1, 5, 8, 1, .... Xn1*10 + 1, Xn1*10 + 4, Xn1*10 + 7, X(n2*10+1) + 1, X(n2*10+1) + 5, X(n2*10+1) +8, ...
Such that N is the set of all Positive Intergers
So the series: 1, 4, 7, 11, 15, 18, 21, 24, 27, 31, 35, 38, 41, 44, 47, 51,
is infinite and consistent. There can be other Super Sets which contain the original Sub Set. If fact, it can be shown mathematically that there are an Infinite amount of Super Sets that contain the given Sub Set.