A049514 - OEIS

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

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OFFSET

1,1

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for sequences related to the number Pi

EXAMPLE

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)

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 *)

PROG

(Haskell)

a049514 n = a049514_list !! (n-1)

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

-- Reinhard Zumkeller, Mar 12 2015

(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

CROSSREFS

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

Cf. A000796, A095916.

Sequence in context: A101066 A340121 A061442 * A049518 A334146 A133633