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Search: id:A152042
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| A152042 |
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Digit base ten of an "almost Pi" BBP type solution in base 24 digits: a=Sum[((1/24^n)*(5/(12*n + 1) + (-1)/(12*n + 2) + (-4)/(12n + 3) + (-3)/(12*n + 5) + 4/(12*n + 7)) + 3*(1/24^n)*(0/(12*n + 1) + ( 5)/(12*n + 2) + (1)/(12n + 3) + (0)/( 12*n + 5) + 2/(12*n + 7)))/4, {n, 0, Infinity}]. |
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1
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| 3, 1, 4, 1, 5, 9, 3, 8, 2, 9, 9, 8, 4, 1, 9, 5, 1, 1, 7, 0, 6, 0, 6, 5, 3, 3, 4, 4, 1, 6, 6, 7, 8, 2, 5, 8, 5, 1, 6, 3, 8, 7, 2, 1, 4, 8, 0, 4, 8, 7, 7, 4, 7, 9, 4, 5, 4, 5, 4, 8, 0, 0, 3, 6, 3, 0, 8, 7, 6, 9, 9, 2, 0, 0, 5, 7, 7, 9, 6, 1, 4, 0, 0, 1, 0, 7, 6, 2, 5, 7, 3, 3, 1, 7, 5, 7, 6, 9, 6, 5, 0, 3, 0, 3, 4
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OFFSET
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0,1
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COMMENT
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The importance of such numbers existing comes from quantum cosmology: multi-universe theory. The idea is that other universe exist with just slightly different fundamental constants. This Pi' is off by 1.176394401878598009960887279700966702748673668973570535444000953513771587 141382727747975459897048192046563857573233257176765089074353711041159774315514 6969232516251485664960116939921016403816145339191524304`193.5734029138387*10^-6.
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FORMULA
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a=Sum[((1/24^n)*(5/(12*n + 1) + (-1)/(12*n + 2) + (-4)/(12n + 3) + (-3)/(12*n + 5) + 4/(12*n + 7)) + 3*(1/24^n)*(0/(12*n + 1) + ( 5)/(12*n + 2) + (1)/(12n + 3) + (0)/( 12*n + 5) + 2/(12*n + 7)))/4, {n, 0, Infinity}]. Simplified version: FullSimplify[((1/24^n)*(5/(12*n + 1) + (-1)/( 12*n + 2) + (-4)/(12n + 3) + (-3)/(12*n + 5) + 4/(12*n + 7)) + 3*(1/ 24^n)*(0/(12*n + 1) + (5)/(12*n + 2) + (1)/(12n + 3) + (0)/(12*n + 5) + 2/(12*n + 7)))/4]= 2^(-1-3*n)*3^(-1-n)*(656 + 11793 n + 67932 n^2 + 157680 n^3 + 129600 n^4)/(1 + 4 n) (1 + 6 n) (1 + 12 n) (5 + 12 n) (7 + 12 n).
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MATHEMATICA
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a=Sum[((1/24^n)*(5/(12*n + 1) + (-1)/(12*n + 2) + (-4)/(12n + 3) + (-3)/(12*n + 5) + 4/(12*n + 7)) + 3*(1/24^n)*(0/(12*n + 1) + ( 5)/(12*n + 2) + (1)/(12n + 3) + (0)/( 12*n + 5) + 2/(12*n + 7)))/4, {n, 0, Infinity}]; Table[Mod[Floor[a*10^n], 10], {n, 0, 200}]
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CROSSREFS
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Sequence in context: A114609 A068089 A068079 this_sequence A057466 A086183 A014462
Adjacent sequences: A152039 A152040 A152041 this_sequence A152043 A152044 A152045
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 21 2008
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