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A049534 Starting index of a string of 6 or more consecutive equal digits in decimal expansion of Pi.

%I A049534 #25 Mar 21 2017 18:33:11
%S A049534 763,193035,222300,244454,252500,253210,255946,399580,419998,452072,
%T A049534 710101,828500,963025,1006928,1129020,1264271,1637081,1691164,1699928,
%U A049534 1722777,1795774,1985814,2309219,2328784,2376568,2418534,2523357
%N A049534 Starting index of a string of 6 or more consecutive equal digits in decimal expansion of Pi.
%C A049534 Digits 3,1,4,... are indexed 1,2,3,... (in contrast to, e.g., A083600 - A083645).
%C A049534 The successive strings are 6 nines, 6 nines, 6 eights, 6 fives, 6 sixes, 6 fives, 6 ones, 6 sevens, 6 fives, 6 sevens, 7 threes, 6 fours, 6 twos, 6 sevens, 6 threes, 6 fours, 6 twos, 6 fours, 6 zeros, 7 nines, 6 twos, 6 nines, 6 sevens, 6 zeros, 6 sevens, 6 eights, 6 twos, 6 zeros, 6 ones, 6 nines, 6 eights, 6 nines, 6 eights, 7 threes, 6 ones, 6 fours, 6 fours, 7 sevens, 7 nines, 6 twos, 7 fives, 6 nines, 6 fours, 6 eights, 7 sevens, 7 zeros, 6 sixes, 6 threes, 6 sixes, 7 nines, 6 sevens, 6 threes, 7 ones, 7 eights, ..., . - _Robert G. Wilson v_, Aug 28 2006
%C A049534 If there are more than 6 equal digits starting at a(n), then a(n)+1 etc. is not listed, in contrast to, e.g., A083600 - A083645, and most other sequences of this type. Therefore the sequence data yields only candidates for longer runs, but they cannot be deduced from the data as this sequence can be deduced from consecutive numbers in A049517, cf. formula. - _M. F. Hasler_, Mar 21 2017
%H A049534 David G. Andersen, <a href="http://www.angio.net/pi/piquery">The Pi-Search Page</a>.
%H A049534 <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%F A049534 Union of A083600, A083604, A083609, A083613, A083618, A083623, A083628, A083634, A083640, and A083645, plus one (because of indexing convention), and consecutive numbers removed in each of the sets. Also, { A049517(n) | A049517(n+1) = A049517(n)+1, but not A049517(n-1) = A049517(n)-1 } = { n+1 | (floor(Pi*10^n) mod 10^6) mod 111111 = 0, but not for n-1 }, where mod is the binary "remainder" operator. - _M. F. Hasler_, Mar 21 2017
%t A049534 p = RealDigits[Pi, 10, 2645268][[1]]; Select[ Range@2645263, p[[ # ]] == p[[ # + 1]] == p[[ # + 2]] == p[[ # + 3]] == p[[ # + 4]] == p[[ # + 5]] &]; (* _Robert G. Wilson v_, Aug 28 2006 *)
%Y A049534 Cf. A049514, A049515, A049516, A049517: starting positions of 2, 3, 4, 5 consecutive equal digits; A049518, A049519, A049520, A049521: exactly 2, 3, 4, 5 consecutive equal digits, A049522, A049523: first occurrence of (at least / exactly) n consecutive equal digits.
%Y A049534 Cf. A083600, A083604, A083609, A083613, A083618, A083623, A083628, A083634, A083640, and A083645: starting positions of 6 consecutive '0's, ..., '9's.
%Y A049534 Cf. A049517: starting position of 5 or more consecutive equal digits.
%K A049534 nonn,base
%O A049534 1,1
%A A049534 _Harvey P. Dale_
%E A049534 Entry revised by _N. J. A. Sloane_, Aug 26 2006
%E A049534 More terms from _Robert G. Wilson v_, Aug 28 2006