# Maple program for A068827:
# number of digits in n
A055642 := proc(n)
	max(1,1+ilog10(n)) ;
end proc:

# intial digit of n
A000030 := proc(n)
	if n = 0 then
		0;
	else
		op(-1,convert(n,base,10)) ;
	end if;
end proc:

# concatenate all members of the list L
catL := proc(L)
	local a,i,nds;
	a := op(1,L) ;
	for i from 2 to nops(L) do
		nds := A055642(op(i,L)) ;
		a := 10^nds*a+op(i,L) ;
	end do;
	a;
end proc:

# return allowed digit range for digit following prevdig
A068827aux := proc(prevdig)
	local digmin,digmax ;
	if prevdig = 9 then
		digmin := 1 ;
		digmax := 8 ;
	else
		digmin := prevdig+1 ;
		digmax := 9 ;
	end if;
	return [digmin,digmax] ;
end proc:

# check whether the digits of a, starting with the 2nd, are an allowed sequence
isA068827aux := proc(a)
	local dgs,drange,i ;
	dgs := convert(a,base,10) ; # list digits right to left
	for i from 2 to nops(dgs) do
		drange := A068827aux(op(1-i,dgs)) ;
		if op(-i,dgs) < op(1,drange) or op(-i,dgs) > op(2,drange) then
			return false;
		end if;
	end do:
	return true;
end proc:

# compute A068827(n)
A068827 := proc(n)
	option remember;
	local a,pdig,drange;
	if n = 1 then
		2;
	else
		# last digit of the previous a(n-1)
		pdig := procname(n-1) mod 10 ;
		drange := A068827aux(pdig) ;

		# next a(n) must be prime...
		a := nextprime(procname(n-1)) ;
		while true do
			if A000030(a) >= op(1,drange) and A000030(a) <= op(2,drange) then
				if isA068827aux(a) then
					return a;
				end if;
			end if;
			a := nextprime(a) ;
		end do:
	end if;
end proc:
seq(A068827(n),n=1..80) ;


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