For both of the following, no integer linear relations appear to exist. table of "Wilsonian sums" of 1/sqrt(1+j) for each j=1..32: j SUM( h(n) / sqrt(n+j) for n=0..2^k-1 in limit of large k --- ----------------------------------------------------------- 1 0.1983140804979377 2 0.0648679674894559 3 0.0294926839418280 4 0.0157413778643092 5 0.0092727250186152 6 0.0058468071083846 7 0.0038768346692010 8 0.0026728045984540 9 0.0019012236938776 10 0.0013876178483701 11 0.0010348719377425 12 0.0007861585985739 13 0.0006068222719239 14 0.0004749802427539 15 0.0003763975850233 16 0.0003015724778226 17 0.0002440176120376 18 0.0001992145334106 19 0.0001639596428052 20 0.0001359450434934 21 0.0001134839819466 22 0.0000953274430131 23 0.0000805394456847 24 0.0000684108748084 25 0.0000583990578796 26 0.0000500848191169 27 0.0000431415737542 28 0.0000373128299688 29 0.0000323956358195 30 0.0000282282789730 31 0.0000246810617323 32 0.0000216493224597 No linear relations found. table of "Wilsonian sums" of 1/sqrt(1+j) for each j=0..32: j SUM( h(n) / sqrt(n+j) for n=0..2^k-1 in limit of large k --- ----------------------------------------------------------- 0 -0.6340742633208627 1 -0.1087899444969256 2 -0.0515209115743647 3 -0.0294697315032235 4 -0.0186280444431191 5 -0.0125570333423308 6 -0.0088605088234095 7 -0.0064719521202861 8 -0.0048578149370044 9 -0.0037278911614336 10 -0.0029139993988712 11 -0.0023136758922906 12 -0.0018619065384380 13 -0.0015160228631279 14 -0.0012472097270808 15 -0.0010355247113232 16 -0.0008668689001796 17 -0.0007310847509929 18 -0.0006207330180334 19 -0.0005302837800949 20 -0.0004555701919706 21 -0.0003934154098761 22 -0.0003413704416433 23 -0.0002975279275219 24 -0.0002603886226424 25 -0.0002287648004256 26 -0.0002017072431677 27 -0.0001784519084129 28 -0.0001583801579947 29 -0.0001409873564580 30 -0.0001258597327007 31 -0.0001126559549967 32 -0.0001010928558065 No linear relations found.