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Formula Formulation (Posted on 2014-03-03) Difficulty: 3 of 5
A function f(N) is defined as:
f(1)=sod(12), f(2) = sod(122)
f(3) = sod(1212), f(4) = sod(12122), .... and, so on

Derive the general formula for f(N) in terms of N.

*** sod(x) denotes the sum of the digits of base ten expansion of x.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: first few -- larger n Comment 4 of 4 |
(In reply to first few by Charlie)

  n      f(n)    sqrt(f(n))   
 41      355  18.8414436814167719444
 42      369  19.2093727122985460594
 43      370  19.2353840616713447518
 44      396  19.8997487421323990946
 45      385  19.6214168703485834684
 46      405  20.1246117974981072676
 47      400  20.0
 48      432  20.7846096908265275222
 49      424  20.5912602819740006315
 50      450  21.2132034355964257319
 51      439  20.9523268397569628977
 52      468  21.6333076527839357587
 53      463  21.517434791350013523
 54      486  22.0454076850486028837
 55      478  21.8632111090754461479
 56      504  22.4499443206436483135
 57      502  22.405356502408079291
 58      522  22.8473193175917248569
 59      517  22.7376340018041454971
 60      540  23.237900077244501311
 61      541  23.2594066992260144365
 62      558  23.622023622035433059
 63      547  23.3880311270529995418
 64      567  23.8117617995813153145
 65      562  23.7065391822593961686
 66      594  24.3721152139078810813
 67      577  24.0208242989286277323
 68      603  24.5560583156173499098
 69      592  24.3310501211928787559
 70      630  25.0998007960222664393
 71      616  24.8193472919817131922
 72      648  25.4558441227157108783
 73      631  25.1197133741609400553
 74      666  25.8069758011278803151
 75      655  25.5929677841394548963
 76      684  26.1533936612440413134
 77      670  25.8843582110895691413
 78      702  26.4952825989835405642
 79      694  26.3438797446389813267
 80      720  26.8328157299974763568
 81      709  26.6270539113886949744
 82      738  27.1661554144122498797
 83      733  27.0739727413617671315
 84      756  27.4954541697350400395
 85      739  27.1845544381363734721
 86      765  27.6586333718786619299
 87      754  27.4590604354919616757
 88      792  28.1424945589405773273
 89      769  27.7308492477240948993
 90      801  28.3019433961698114339
 91      784  28.0
 92      828  28.7749891398763172495
 93      808  28.4253408071037909939
 94      846  29.0860791444979740844
 95      823  28.6879765755621042894
 96      864  29.3938769133981371783
 97      847  29.1032644217104964954
 98      882  29.6984848098349960247
 99      862  29.3598365118063966374
 100     900  30.0
 101     886  29.7657521322744337603
 102     918  30.29851481508623386
 103     901  30.0166620396072687634
 104     936  30.5941170815567089801
 105     925  30.4138126514910984449
 106     954  30.8868904229610009473
 107     931  30.5122926047847148656
 108     963  31.0322412983658014091
 109     946  30.7571129984593970181
 110     990  31.4642654451045464097
 111     961  31.0
 112     999  31.6069612585582165451
 113     976  31.2409987036266175765
 114     1026  32.0312347560939336324
 115     1000  31.6227766016837933199
 116     1044  32.3109888428070241874
 117     1015  31.8590646441479822676
 118     1062  32.5883414736006471716
 119     1039  32.2335229225723944913
 120     1080  32.8633534503099668073

  Posted by Charlie on 2014-03-03 17:27:31
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