cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A049514 #19 Oct 18 2019 21:33:13
%S A049514 25,35,45,60,80,95,118,126,131,136,154,155,175,178,179,183,186,202,
%T A049514 205,212,216,218,231,258,277,283,308,310,316,318,323,361,363,365,373,
%U A049514 378,396,402,428,438,446,454,460,473,485,495,504,508,512,517,536,560,593
%N A049514 Starting index of a string of 2 or more consecutive equal digits in decimal expansion of Pi.
%C A049514 Digits 3,1,4,... are indexed 1,2,3,...
%C A049514 A095916(a(n)) = 0. - _Reinhard Zumkeller_, Mar 12 2015
%C A049514 See A049518 for the "exactly 2" variant, which differs from a(11) on. - _M. F. Hasler_, Oct 18 2019
%H A049514 Reinhard Zumkeller, <a href="/A049514/b049514.txt">Table of n, a(n) for n = 1..1000</a>
%H A049514 <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%e A049514 From _M. F. Hasler_, Oct 18 2019: (Start)
%e A049514 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 A049514 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 A049514 ConsecutiveOccurrences1[alist_, n_] := Flatten @ Position[ Apply[ SameQ, Partition[ alist, n, 1], {1}], True]; ConsecutiveOccurrences1[ First[ RealDigits[Pi, 10, 601]], 2]
%t A049514 Flatten[Position[Partition[RealDigits[Pi,10,1000][[1]],2,1],_?(#[[1]] == #[[2]]&),{1},Heads->False]] (* _Harvey P. Dale_, Dec 21 2014 *)
%t A049514 SequencePosition[RealDigits[Pi,10,1000][[1]],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Mar 30 2019 *)
%o A049514 (Haskell)
%o A049514 a049514 n = a049514_list !! (n-1)
%o A049514 a049514_list = filter ((== 0) . a095916) [1..]
%o A049514 -- _Reinhard Zumkeller_, Mar 12 2015
%o A049514 (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 A049514 Cf. A049515, A049516, A049517, A049518, A049519, A049520, A049521, A049522, A049523.
%Y A049514 Cf. A000796, A095916.
%K A049514 nonn,base
%O A049514 1,1
%A A049514 _Harvey P. Dale_
%E A049514 Edited by _Robert G. Wilson v_, May 09 2003