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.

Showing 1-3 of 3 results.

A083629 Starting positions of strings of seven 6's in the decimal expansion of Pi.

Original entry on oeis.org

8209165, 18696860, 19715001, 45681781, 45681782, 45681783, 46991724, 53280671, 55494960, 55616210, 55616211, 58285372, 62663646, 79245087, 101059334, 103078590, 105264397, 107986645, 108304062, 129423072, 129423073, 138606784, 159863007, 160301327, 160301328, 160524078
Offset: 1

Views

Author

Rick L. Shepherd, May 04 2003

Keywords

Crossrefs

Cf. A083628 (six 6's), A083630 (eight 6's).

Extensions

More terms from Rick L. Shepherd, Aug 07 2006
More terms from Jinyuan Wang, Mar 01 2020

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

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

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

A083627 Starting positions of strings of five 6's in the decimal expansion of Pi.

Original entry on oeis.org

48439, 102387, 140744, 250129, 252499, 252500, 309379, 363995, 375601, 450347, 483202, 595298, 722275, 850138, 964604, 1109283, 1268703, 1367754, 1373818, 1381298, 1676919, 1717341, 1819654, 1901872, 1924024, 2088622, 2162433
Offset: 1

Views

Author

Rick L. Shepherd, May 03 2003

Keywords

Crossrefs

Cf. A083626 (four 6's), A083628 (six 6's).

Programs

  • Mathematica
    SequencePosition[RealDigits[Pi,10,2163000][[1]],{6,6,6,6,6}][[All,1]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 12 2019 *)
Showing 1-3 of 3 results.