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

25, 35, 45, 60, 80, 95, 118, 126, 131, 136, 154, 155, 175, 178, 179, 183, 186, 202, 205, 212, 216, 218, 231, 258, 277, 283, 308, 310, 316, 318, 323, 361, 363, 365, 373, 378, 396, 402, 428, 438, 446, 454, 460, 473, 485, 495, 504, 508, 512, 517, 536, 560, 593

Offset: 1

Author

Harvey P. Dale

Keywords

• nonn
• base

Comments

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

A095916(a(n)) = 0. - Reinhard Zumkeller, Mar 12 2015

See A049518 for the "exactly 2" variant, which differs from a(11) on. - M. F. Hasler, Oct 18 2019

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to the number Pi

Crossrefs

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

Cf. A000796, A095916.

Programs

Haskell

a049514 n = a049514_list !! (n-1)
a049514_list = filter ((== 0) . a095916) [1..]
-- Reinhard Zumkeller, Mar 12 2015

Mathematica

ConsecutiveOccurrences1[alist_, n_] := Flatten @ Position[ Apply[ SameQ, Partition[ alist, n, 1], {1}], True]; ConsecutiveOccurrences1[ First[ RealDigits[Pi, 10, 601]], 2]
Flatten[Position[Partition[RealDigits[Pi,10,1000][[1]],2,1],?(#[[1]] == #[[2]]&),{1},Heads->False]] (* _Harvey P. Dale, Dec 21 2014 *)
SequencePosition[RealDigits[Pi,10,1000][[1]],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 30 2019 *)

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

Extensions

Edited by Robert G. Wilson v, May 09 2003