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A079164
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Twin-primorial numbers: running products of twin primes.
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5
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3, 15, 75, 525, 5775, 75075, 1276275, 24249225, 703227525, 21800053275, 893802184275, 38433493923825, 2267576141505675, 138322144631846175, 9820872268861078425, 716923675626858725025, 72409291238312731227525
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OFFSET
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1,1
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COMMENTS
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The sum of the reciprocals converges to 0.4154254016622336549103692152614908366885449298862362851444631680740051...
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LINKS
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EXAMPLE
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The first two twin primes are 3 and 5, so the first term is 3 and the second term is 15. The next two twin primes are 5 and 7, so the third term is 5*15=75 and the fourth term is 75*7=525
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MATHEMATICA
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Rest[FoldList[Times, 1, Flatten[Select[Partition[Prime[Range[30]], 2, 1], Last[#]-First[#]==2&]]]] (* Harvey P. Dale, Mar 16 2011 *)
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PROG
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(PARI) twprfact(n) = {sr=0; tp = vector(10000); k=1; forprime(j = 3, n, if(nextprime(j+1)-j == 2, tp[k] = j; tp[k+1] = j+2; k+=2; ); ); for(j=1, k-1, y=1; for(i = 1, j, y*=tp[i]; ); print1(y", "); sr+=1.0/y; ); print(); print(sr); }
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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EXTENSIONS
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Definition clarified and example provided by Harvey P. Dale, Mar 16 2011
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STATUS
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approved
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