A235589 The periodic part of the decimal expansion of m/(m+1), for those m/(m+1) that have pure periods.

6, 857142, 8, 90, 923076, 9411764705882352, 947368421052631578, 952380, 9565217391304347826086, 962, 9655172413793103448275862068, 967741935483870, 96, 972, 974358, 97560, 976744186046511627906, 9787234042553191489361702127659574468085106382, 979591836734693877551020408163265306122448

Offset: 1

Author

Bill McEachen, Jan 12 2014

Keywords

• nonn
• base

Comments

A companion sequence stemming from the some of the elements excluded by A156703. The sequence is highly volatile and infinite...as with A156703 the subset elements are encountered in numerical order. a(n) will start with the digit 9 for n>4 I believe. Entries can grow quite large very quickly. Each entry will be encountered once, and they will end in an even digit.

The number of digits of a(n) is given by A002329. - Michel Marcus, Aug 19 2015

Examples

			1/2=0.5 non-repeating, so exclude from sequence.
2/3=0.6 repeating, so a(1)=6.
5/6=0.833 (repeating) but has "8" prefix ahead of repeating "3" so exclude from sequence (decimal expansion not purely periodic)
6/7=0.857142 repeating so a(2)=857142.
		

Crossrefs

Subsequence of A259299.

Cf. A156703, A036275, A060283, A114205.

Programs

Mathematica

FromDigits@ Flatten@ First@ RealDigits[(# - 1)/#] & /@ Select[Range@ 120, CoprimeQ[#, 10] &] //Rest (* Michael De Vlieger, Aug 18 2015 *)

Formula

a(n) = the periodic part of the decimal expansion of (A045572(n+1)-1) / A045572(n+1). - Doug Bell, Aug 17 2015

Extensions

Missing terms added by Ralf Stephan, Jan 19 2014

Incorrect terms 916, 94 removed and two more terms added by Michael De Vlieger, Aug 18 2015