cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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
Offset: 1

Views

Author

Harvey P. Dale

Keywords

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

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.

Programs

  • 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 *)

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(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

Extensions

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

A082586 Length of the run of consecutive equal digits in the decimal expansion of Pi beginning at position n and ignoring any immediately-previous equal digits.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
Offset: 1

Views

Author

N. J. A. Sloane, May 12 2003

Keywords

Comments

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

Examples

			Pi = 3.141592653589793238462643383279502884... and the first run of 2 starts at position 25, so a(n) = 1 for n < 25, a(25) = 2.
Runs of length 2 begin in positions 25,35,45,60,80,95 then not again until 118. Compare A049514 and A049518.

Crossrefs

Cf. A084073, A121657 (another version).

Extensions

More terms from Kyle Hoffman (khoffma1(AT)ashland.edu), Apr 01 2004
Definition clarified by Rick L. Shepherd, Aug 26 2006

A277827 Digits that appear twice consecutively in the decimal expansion of Pi, in order of appearance.

Original entry on oeis.org

3, 8, 9, 4, 9, 1, 6, 4, 5, 2, 1, 1, 1, 5, 5, 4, 2, 4, 8, 6, 3, 4, 3, 6, 6, 3, 0, 6, 5, 8, 8, 0, 1, 3, 8, 6, 1, 3, 1, 1, 1, 4, 9, 8, 2, 1, 3, 3, 4, 6, 2, 7, 6, 0, 0, 7, 7, 7, 4, 2, 2, 9, 1, 4, 7, 7, 9, 1, 9, 9, 9, 9, 9, 9, 4, 5, 2, 3, 4, 1, 8, 0, 0, 8, 3, 7, 6, 5, 1, 8, 7, 7, 2, 6, 0, 6, 1, 1, 8, 3
Offset: 1

Views

Author

Bobby Jacobs, Nov 01 2016

Keywords

Comments

A digit d of Pi is in this sequence iff A000796(i) = A000796(i+1), where i is the index of d in A000796. - Felix Fröhlich, Nov 01 2016

Examples

			Pi=3.14159265358979323846264(33)83279502(88)41971693(99)3751058209749(44)592307816406286208(99)8628034825342(11)70679...
Therefore, this sequence starts 3, 8, 9, 4, 9, 1.

Crossrefs

Cf. A000796, A049514.

Programs

  • PARI
    pidigit(n) = floor(Pi*10^n) - 10*floor(Pi*10^(n-1))
terms(n) = my(k=1, i=0); while(1, if(pidigit(k)==pidigit(k+1), print1(pidigit(k), ", "); i++); if(i==n, break); k++)
/* Print initial 100 terms as follows */
terms(100) \\ Felix Fröhlich, Nov 01 2016

Formula

a(n) = A000796(A049514(n)).
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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