OFFSET
1,1
COMMENTS
The number of terms between 2^(n-1) and 2^n-1 is, for n = 1, 2, 3, ...: 0, 0, 0, 2, 6, 17, 24, 69, 129*, 215, 425, 891, 1571, 2994, 5655*, 10535, 20132, 38840, 73510, 140730, 268438*, 514262, ... (For terms with * the next larger power of 2 is in the sequence, so it would be, e.g., ..., 130, 214, ... if we count from 2^n+1 to 2^(n+1).) At 2^22 this corresponds to a density of about 25%, decreasing by about 1% at each power of 2.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Andrew Lohr, Several Topics in Experimental Mathematics, arXiv:1805.00076 [math.CO], 2018.
EXAMPLE
12 = 2^2 + 2^3, 13 = 2^2 + 3^2, 17 = 2^3 + 3^2, ...
MAPLE
N:= 1000: # for all terms <= N
PP:= {seq(seq(x^k, k=2..floor(log[x](N))), x=2..floor(sqrt(N)))}:
sort(convert(select(`<=`, {seq(seq(PP[i]+PP[j], i=1..j-1), j=2..nops(PP))}, N), list)); # Robert Israel, May 27 2018
MATHEMATICA
max = 150; Table[If[x^k == y^m, Nothing, x^k + y^m], {x, 2, Sqrt[max-4]}, {y, x, Sqrt[max-4]}, {k, 2, Log[2, max-4]}, {m, 2, Log[2, max-4]}] // Flatten // Select[#, # <= max &]& // Union (* Jean-François Alcover, Sep 18 2018 *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, May 26 2018
STATUS
approved