Fibostracci
( Stracci is a kind of lasagna – see here : " Al plur., stracci , tipo di pasta fatta in casa, tagliata in forma di lasagne di cui è anche simile l’impasto, rammorbidito però con un po’ di latte o di olio; è in uso spec. in Liguria e nel Piemonte".) We start S with a(1) = 0 and a(2) = 1. As 0 and 1 share no digit we add them and extend S with the sum : S = 0, 1, 1 , … As the last two integers share at least one digit, we don’t add them and extend S instead with the smallest integer not yet in S : S = 0, 1, 1, 2 , … As 1 and 2 share no digit, we add them and extend S with the sum : S = 0, 1, 1, 2, 3 , … As 2 and 3 share no digit, we add them and extend S with the sum : S = 0, 1, 1, 2, 3, 5 , … Then: S = 0, 1, 1, 2, 3, 5, 8, 13, 21 , … As the last two integers share at least one digit, we don’t add them and extend S instead with the smallest integer not yet in S : S = 0, 1, 1, 2, 3, 5, 8, 13, 21, 4 , … Then : S = 0, 1, 1, 2, 3, 5, 8, 13, 21, 4, 25, 29 ,...