Monthly Archives: February 2013

From Prime —> Square —> Prime

                  2 || 3   =   23   is a prime number                         ||                         \/              (2^2) || (3^2)   =   49   is a perfect square    (= 7^2)                         ||                         \/              (4^2) || … Continue reading

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0.2000 2001 2002 2003 2004 …. 2013 ….

19998001   =   17 * 1176353 99980001   =   9999^2     19998001 / 99980001   =   0.200020012002200320042005200620072008200920102011201220132014201520162017 201820192020202120222023202420252026202720282029203020312032203320342035 203620372038203920402041204220432044204520462047204820492050205120522053 205420552056205720582059206020612062206320642065206620672068206920702071 207220732074207520762077207820792080208120822083208420852086208720882089 209020912092209320942095209620972098209921002101210221032104210521062107 210821092110211121122113211421152116211721182119212021212122212321242125 212621272128212921302131213221332134213521362137213821392140214121422143 214421452146214721482149215021512152215321542155215621572158215921602161 216221632164216521662167216821692170217121722173217421752176217721782179 218021812182218321842185218621872188218921902191219221932194219521962197 219821992200220122022203220422052206220722082209221022112212221322142215 221622172218221922202221222222232224222522262227222822292230223122322233 223422352236223722382239224022412242224322442245224622472248224922502251 225222532254225522562257225822592260226122622263226422652266226722682269 227022712272227322742275227622772278227922802281228222832284228522862287 228822892290229122922293229422952296229722982299230023012302230323042305 230623072308230923102311231223132314231523162317231823192320232123222323 232423252326232723282329233023312332233323342335233623372338233923402341 234223432344234523462347234823492350235123522353235423552356235723582359 … Continue reading

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Num3er 0.2013……..

x/y   =   0.2013……..   46304562   =   2 * 3 * 7717427 229933099   =   11 * 20903009 46304562 / 229933099   =   0.201382759599999998260363550356010293237512534026256045894462… 1 / 4967   (period 4966)   =   0.000201328769881216025770082544795651298570565733843366217032…   … Continue reading

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0.2013 2012 2011 2010 …..

The consecutive years starting with   2013 in descending order:   20127986   =   2 * 2801 * 3593 99980001   =   9999^2   20127986 / 99980001   =   0.201320122011201020092008200720062005200420032002200120001999199819971996 1995199419931992199119901989198819871986198519841983198219811980197919781977 1976197519741973197219711970196919681967196619651964196319621961196019591958 1957195619551954195319521951195019491948194719461945194419431942194119401939 1938193719361935193419331932193119301929192819271926192519241923192219211920 1919191819171916191519141913191219111910190919081907190619051904190319021901 1900189918981897189618951894189318921891189018891888188718861885188418831882 1881188018791878187718761875187418731872187118701869186818671866186518641863 … Continue reading

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Prime Num3ers| (a+b+c) and (a*b*c) end with digit 7

Goal: To find three different prime numbers   A, B, C   so that their sum   (A + B + C)   and their product   A*B*C   end with the digit 7     For example,   3 … Continue reading

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Square Num3ers| aba… ± 1 is a square

Let’s look at numbers of the form   aba ± 1,   ababa ± 1,   ababab ± 1,   aaabbbccc ± 1   and other combinations   (a ≠ b) For example, aba + 1   is a square: … Continue reading

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Puzzle| 8-digit square number

Find an 8-digit square number which can be transformed into another square when the second digit from the left is increased by   1.                  

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Puzzle| square numbers – DigitSum

Here are 7 consecutive squares for each of which its decimal digits sum to a square: 9^2  =  81                                           … Continue reading

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Puzzle| 12-digit square num3er

Find a 12-digit square number which is the concatenation of a 4-digit square number and an 8-digit square number.     12-digit square number  =  B  ||  C B is either a 4-digit square or an 8-digit square.     … Continue reading

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9-digit num3er aaabbbccc

Find a 9-digit number of the form   aaabbbccc   so that              aaabbbccc   +   1    is a square number   that is,        aaabbbccc   +   1   =   x^2     @InfinitelyManic found: … Continue reading

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