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A049518 Starting index of a string of exactly 2 consecutive equal digits in the decimal expansion of Pi. 7

%I #10 Oct 18 2019 21:33:20

%S 25,35,45,60,80,95,118,126,131,136,175,183,186,202,205,212,216,218,

%T 231,258,277,283,308,310,316,318,323,361,363,365,373,378,396,402,428,

%U 438,446,454,460,473,485,495,504,508,512,517,536,560,593,622

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

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

%C See A049514 for the variant "at least 2", which differs from a(11) on. - _M. F. Hasler_, Oct 18 2019

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

%e The integer part of Pi*10^22 ends in 33, i.e., at position 22 starts the (first) string of two repeated digits 3, therefore a(1) = 22.

%e At position 154 starts a string of three '1's, so sequence A049514 lists both, 154 and 155, but this sequence lists none of these. (End)

%t Flatten[Position[Partition[RealDigits[Pi,10,1000][[1]],4,1],_?(#[[1]] != #[[2]] && #[[2]]==#[[3]]&&#[[3]]!=#[[4]]&),1,Heads->False]]+1 (* _Harvey P. Dale_, Jul 08 2017 *)

%o (PARI) A049518_upto(N=999)={default(realprecision, N); my(p=digits(Pi\10^-N)); select(i->p[i]==p[i+1] && p[i]!=p[i-1] && p[i]!=p[i+2], [9..N-2])} \\ _M. F. Hasler_, Oct 18 2019

%Y Cf. A049514-A049523.

%K nonn,base

%O 0,1

%A _Harvey P. Dale_

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Last modified April 24 20:05 EDT 2024. Contains 371963 sequences. (Running on oeis4.)