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#0[#+1/If[++i#>1,-Echo@i,i]]&[i=1] Outputs the sequence indefinitely (up to $IterationLimit, 4096 by default).
Subtracts terms from 1 instead of adding from 0.
Without overriding $IterationLimit, 40 bytes:
i=0;Do[i+=1/If[i>1/j,-Echo@j,j],{j,∞}] #0[#+1/If[++i#>1,-Echo@i,i]]&[i=1] Outputs the sequence indefinitely (up to $IterationLimit, 4096 by default).
Without overriding $IterationLimit, 40 bytes:
i=0;Do[i+=1/If[i>1/j,-Echo@j,j],{j,∞}] #0[#+1/If[++i#>1,-Echo@i,i]]&[i=1] Outputs the sequence indefinitely (up to $IterationLimit, 4096 by default).
Subtracts terms from 1 instead of adding from 0.
Without overriding $IterationLimit, 40 bytes:
i=0;Do[i+=1/If[i>1/j,-Echo@j,j],{j,∞}] #0[#+1/If[++i#>1,-Echo@i,i]]&[i=1] Outputs the sequence indefinitely (up to $IterationLimit, 4096 by default).
Without overriding $IterationLimit, 40 bytes:
i=0;Do[i+=1/If[i>1/j,-Echo@j,j],{j,∞}]