

A049534


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


3



763, 193035, 222300, 244454, 252500, 253210, 255946, 399580, 419998, 452072, 710101, 828500, 963025, 1006928, 1129020, 1264271, 1637081, 1691164, 1699928, 1722777, 1795774, 1985814, 2309219, 2328784, 2376568, 2418534, 2523357
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OFFSET

1,1


COMMENTS

Digits 3,1,4,... are indexed 1,2,3,... (in contrast to, e.g., A083600  A083645).
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
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


LINKS

Table of n, a(n) for n=1..27.
David G. Andersen, The PiSearch Page.
Index entries for sequences related to the number Pi


FORMULA

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(n1) = A049517(n)1 } = { n+1  (floor(Pi*10^n) mod 10^6) mod 111111 = 0, but not for n1 }, where mod is the binary "remainder" operator.  M. F. Hasler, Mar 21 2017


MATHEMATICA

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 *)


CROSSREFS

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.
Cf. A083600, A083604, A083609, A083613, A083618, A083623, A083628, A083634, A083640, and A083645: starting positions of 6 consecutive '0's, ..., '9's.
Cf. A049517: starting position of 5 or more consecutive equal digits.
Sequence in context: A049517 A121321 A084072 * A245007 A204356 A238920
Adjacent sequences: A049531 A049532 A049533 * A049535 A049536 A049537


KEYWORD

nonn,base


AUTHOR

Harvey P. Dale


EXTENSIONS

Entry revised by N. J. A. Sloane, Aug 26 2006
More terms from Robert G. Wilson v, Aug 28 2006


STATUS

approved



