Progressive progressions

An arithmetic progression is a sequence of numbers a1, a2,... an such that ai+1-ai is equal for all 0≤iNow consider a sequence of arithmetic progressions A1 = (a1,1, a1,2,... a1,n1), A2 = (a2,1, a2,2,... a2,n2),... Ak = (ak,1, ak,2,... ak,nk) A progressive progression is such a sequence with the additional properties that: - ai,ni = ai+1,1 for 1 ≤ i i, the common difference of Ai, is a positive