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A049514 Starting index of a string of 2 or more consecutive equal digits in decimal expansion of Pi. 14

%I #19 Oct 18 2019 21:33:13

%S 25,35,45,60,80,95,118,126,131,136,154,155,175,178,179,183,186,202,

%T 205,212,216,218,231,258,277,283,308,310,316,318,323,361,363,365,373,

%U 378,396,402,428,438,446,454,460,473,485,495,504,508,512,517,536,560,593

%N Starting index of a string of 2 or more consecutive equal digits in decimal expansion of Pi.

%C Digits 3,1,4,... are indexed 1,2,3,...

%C A095916(a(n)) = 0. - _Reinhard Zumkeller_, Mar 12 2015

%C See A049518 for the "exactly 2" variant, which differs from a(11) on. - _M. F. Hasler_, Oct 18 2019

%H Reinhard Zumkeller, <a href="/A049514/b049514.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>

%e From _M. F. Hasler_, Oct 18 2019: (Start)

%e The integer part of Pi*10^25 ends in 33, i.e., at position 25 starts the (first) string of two repeated digits 3, therefore a(1) = 25.

%e At position 154 starts a string of three '1's, so this sequence lists both, 154 and 155, but sequence A049518 lists none of these. (End)

%t ConsecutiveOccurrences1[alist_, n_] := Flatten @ Position[ Apply[ SameQ, Partition[ alist, n, 1], {1}], True]; ConsecutiveOccurrences1[ First[ RealDigits[Pi, 10, 601]], 2]

%t Flatten[Position[Partition[RealDigits[Pi,10,1000][[1]],2,1],_?(#[[1]] == #[[2]]&),{1},Heads->False]] (* _Harvey P. Dale_, Dec 21 2014 *)

%t SequencePosition[RealDigits[Pi,10,1000][[1]],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 30 2019 *)

%o (Haskell)

%o a049514 n = a049514_list !! (n-1)

%o a049514_list = filter ((== 0) . a095916) [1..]

%o -- _Reinhard Zumkeller_, Mar 12 2015

%o (PARI) A049514_upto(N=999)={default(realprecision,N); my(p=digits(Pi\10^-N)); select(i->p[i]==p[i+1], [9..N-1])} \\ _M. F. Hasler_, Oct 18 2019

%Y Cf. A049515, A049516, A049517, A049518, A049519, A049520, A049521, A049522, A049523.

%Y Cf. A000796, A095916.

%K nonn,base

%O 1,1

%A _Harvey P. Dale_

%E Edited by _Robert G. Wilson v_, May 09 2003

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Last modified September 8 18:41 EDT 2024. Contains 375753 sequences. (Running on oeis4.)