differences of two prime powers

[N. J. A. Sloane]

I am adding these 4 sequences.  They have been mentioned several times
on this mailing list by several correspondents.  Could people check
and extend them please?     Neil

%I A075788
%S A075788 3,3,2,2,3,0,4,4,6,13,3,4,7,0,4,5,5,3,3,6,5,7,3,7,5,3,6,2,15
%N A075788 If n can be written in the form r^i-s^j (see A074981), where r,s,i,j are integers with r>0, s>0, i>1, j>1 choose the representation with smallest r^i (in case of ties, minimize i and j); or if n is not of this form set r=s=i=j=0; sequence gives values of r.
%C A075788 The zeros are only conjectures (cf. A074981).
%C A075788 Use 4^2 rather than 2^4, etc.
%e A075788 1 = 3^2 - 2^3, 2 = 3^3 - 5^2, 3 = 2^2 - 1^2, 4 = 2^3 - 2^2, etc.
%O A075788 0,1
%K A075788 nonn,hard,more
%A A075788 Zakir F. Seidov (seidovzf at yahoo.com), Oct 13 2002

%I A075789
%S A075789 2,3,2,3,2,0,2,2,2,3,3,2,2,0,2,2,2,3,3,2,2,2,3,2,3,3,2,5,2
%N A075789 If n can be written in the form r^i-s^j (see A074981), where r,s,i,j are integers with r>0, s>0, i>1, j>1 choose the representation with smallest r^i (in case of ties, minimize i and j); or if n is not of this form set r=s=i=j=0; sequence gives values of i.
%C A075789 The zeros are only conjectures (cf. A074981).
%C A075789 Use 4^2 rather than 2^4, etc.
%e A075789 1 = 3^2 - 2^3, 2 = 3^3 - 5^2, 3 = 2^2 - 1^2, 4 = 2^3 - 2^2, etc.
%O A075789 0,1
%K A075789 nonn,hard,more
%A A075789 Zakir F. Seidov (seidovzf at yahoo.com), Oct 13 2002

%I A075790
%S A075790 2,5,1,2,2,0,3,2,3,3,4,2,6,0,1,3,2,3,2,4,2,3,2,5,10,1,3,2,14
%N A075790 If n can be written in the form r^i-s^j (see A074981), where r,s,i,j are integers with r>0, s>0, i>1, j>1 choose the representation with smallest r^i (in case of ties, minimize i and j); or if n is not of this form set r=s=i=j=0; sequence gives values of s.
%C A075790 The zeros are only conjectures (cf. A074981).
%C A075790 Use 4^2 rather than 2^4, etc.
%e A075790 1 = 3^2 - 2^3, 2 = 3^3 - 5^2, 3 = 2^2 - 1^2, 4 = 2^3 - 2^2, etc.
%O A075790 0,1
%K A075790 nonn,hard,more
%A A075790 Zakir F. Seidov (seidovzf at yahoo.com), Oct 13 2002

%I A075791
%S A075791 3,2,2,2,2,0,2,3,3,7,2,2,2,0,2,2,3,2,3,2,2,3,2,2,2,2,2,2,2
%N A075791 If n can be written in the form r^i-s^j (see A074981), where r,s,i,j are integers with r>0, s>0, i>1, j>1 choose the representation with smallest r^i (in case of ties, minimize i and j); or if n is not of this form set r=s=i=j=0; sequence gives values of j.
%C A075791 The zeros are only conjectures (cf. A074981).
%C A075791 Use 4^2 rather than 2^4, etc.
%e A075791 1 = 3^2 - 2^3, 2 = 3^3 - 5^2, 3 = 2^2 - 1^2, 4 = 2^3 - 2^2, etc.
%O A075791 0,1
%K A075791 nonn,hard,more
%A A075791 Zakir F. Seidov (seidovzf at yahoo.com), Oct 13 2002