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%I #11 Mar 22 2017 22:03:46
%S 710100,1722776,3204765,3346228,3389380,3517236,3775287,3794572,
%T 4313727,4657555,4722613,5466169,7820866,8209165,9325203,10519242,
%U 12469058,13310436,14233532,14593770,15256174,17893953,18216168,18696860,19175682,19715001,19921876,20202676,22931745,22931746,23189751,23724968,24658601,24658602,24658603
%N Starting position of strings of seven identical digits in the decimal expansion of Pi.
%C Digits 3, 1, 4, ... are indexed 0, 1, 2, ...
%H Dave Andersen, <a href="http://www.angio.net/pi/piquery">Pi-Search Page</a>
%H <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%F Union of A083601, A083605, A118079, A083614, A083619, A083624, A083629, A083635, A083641 and A083646.
%e From the 710100-th decimal on, there are 7 consecutive '3's in Pi's decimal expansion, and there is no earlier occurrence of 7 consecutive identical digits, therefore a(1) = 710100.
%e From the 1722776-th decimal digit on, there are 7 consecutive '9's in Pi's decimal expansion.
%e From the 3204765-th decimal digit on, there are again 7 consecutive '3's.
%e From the 3346228-th decimal digit on, there are 7 consecutive '7's.
%e Further terms correspond to seven '9's at 3389380, '5's at 3517236, '7's at 3775287, '0's at 3794572, '9's at 4313727, '1's at 4657555, '8's at 4722613, '9's at 5466169, '8's at 7820866, '6's at 8209165, '5's at 9325203 and at 10519242, '3's at 12469058, '0's at 13310436, '7's at 14233532, '9's at 14593770 and at 15256174, and finally seven '4's at 17893953 = A083619(1).
%e The first string of seven '2's does not appear until position 82599811 = A118079(1).
%e At position 22931745 there are 8 consecutive '4's, and therefore also 7 '4's starting at 22931746. Similarly, at position 24658601 there are 9 consecutive '7's, therefore the next two terms are 24658602, 24658603.
%Y Cf. A083601, A083605, A118079, A083614, A083619, A083624, A083629, A083635, A083641 and A083646: position of seven '0's, ..., '9's; the disjoint union of these yields this sequence.
%Y Cf. A049534: position of six or more consecutive identical digits, 1-indexed: { a(n)+1 | a(n-1) < a(n)-1 } is a subsequence.
%K nonn,base
%O 1,1
%A _M. F. Hasler_, Mar 21 2017
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