A284166 Starting position of strings of seven identical digits in the decimal expansion of Pi.

710100, 1722776, 3204765, 3346228, 3389380, 3517236, 3775287, 3794572, 4313727, 4657555, 4722613, 5466169, 7820866, 8209165, 9325203, 10519242, 12469058, 13310436, 14233532, 14593770, 15256174, 17893953, 18216168, 18696860, 19175682, 19715001, 19921876, 20202676, 22931745, 22931746, 23189751, 23724968, 24658601, 24658602, 24658603

Offset

1,1

Comments

Digits 3, 1, 4, ... are indexed 0, 1, 2, ...

Links

Table of n, a(n) for n=1..35.

Dave Andersen, Pi-Search Page

Index entries for sequences related to the number Pi

Formula

Union of A083601, A083605, A118079, A083614, A083619, A083624, A083629, A083635, A083641 and A083646.

Example

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.
From the 1722776-th decimal digit on, there are 7 consecutive '9's in Pi's decimal expansion.
From the 3204765-th decimal digit on, there are again 7 consecutive '3's.
From the 3346228-th decimal digit on, there are 7 consecutive '7's.
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).
The first string of seven '2's does not appear until position 82599811 = A118079(1).
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.

Crossrefs

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.

Cf. A049534: position of six or more consecutive identical digits, 1-indexed: { a(n)+1 | a(n-1) < a(n)-1 } is a subsequence.

Sequence in context: A253840 A253934 A083613 * A083614 A346568 A114675

Adjacent sequences: A284163 A284164 A284165 * A284167 A284168 A284169

Keyword

nonn,base

Author

M. F. Hasler, Mar 21 2017

Status

approved