A195835 -id:A195835 - cp's OEIS frontend

A195844 Leaders in the race of digits of e.

2, 8, 2, 9, 7, 2, 3, 9, 2, 7, 4, 7, 9, 3, 9, 3, 9, 3, 9, 3, 9, 2, 6, 7, 3, 9, 3, 7, 6, 7, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 1, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6, 3, 6

Offset: 1

Omar E. Pol, Oct 22 2011

Next term which is different from earlier in A195138.

			The decimal expansion of e = 2.7182818284590452353602... starts with 2 (see A001113) hence the first leader in the race of digits is 2, so a(1) = 2. After 8 stages the new leader is 8 because the number 8 appears three times and the earlier leader appears twice, so a(2) = 8. After 23 stages the new leader is 2 because the number 2 appears five times and the earlier leader appears four times, so a(3) = 2.

Ruediger Jehn, Table of n, a(n) for n = 1..1260

Cf. A001113, A195138, A195835, A195845, A195846, A195847.

More terms from D. S. McNeil, Oct 22 2011

A195847 Leaders in the race of digits of Euler's constant (or Euler-Mascheroni constant) gamma.

Original entry on oeis.org

0, 7, 5, 6, 0, 6, 0, 4, 3, 7, 0, 7, 0, 7, 0, 7, 0, 7, 0, 8, 0, 8, 7, 0, 8, 0, 8, 0, 8, 0, 8, 7, 4, 7, 4, 9, 4, 8, 4, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5

Offset: 1

Omar E. Pol, Oct 22 2011

This is A280811 with repeats removed. - Bobby Jacobs, Jan 12 2017

			The decimal expansion of gamma = 0.5772156649015... starts with 0 hence the first leader in the race of digits is 0, so a(1) = 0.
After four stages the new leader is 7 because the number 7 appears twice and the earlier leader appears once, so a(2) = 7.
After 14 stages the new leader is 5 because the number 5 appears three times and the earlier leader appears twice, so a(3) = 5.

Cf. A001620, A195835, A195844, A195845, A195846, A280811.

More terms from D. S. McNeil, Oct 22 2011

A195845 Leaders in the race of digits of golden ratio phi.

Original entry on oeis.org

1, 8, 2, 6, 2, 8, 4, 8, 4, 6, 4, 8, 6, 2, 7, 2, 0, 1, 7, 3, 7, 1, 7, 1, 7, 1, 0, 7, 0, 7, 0, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 0, 3, 1, 3, 0, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 7, 3, 9

Offset: 1

Omar E. Pol, Oct 22 2011

Next term which is different from earlier in A195139.

			The decimal expansion of golden ratio (phi = 1.6180339887...) starts with 1 (see A001622) hence the first leader in the race of digits is 1, so a(1) = 1. After 10 stages the new leader is 8 because the number 8 appears three times and the earlier leader appears twice, so a(2) = 8.

Cf. A001622, A195139, A195835, A195844, A195846, A195847.

More terms from D. S. McNeil, Oct 22 2011

A195846 Leaders in the race of digits of square root of 2.

Original entry on oeis.org

1, 8, 7, 5, 8, 5, 0, 8, 2, 8, 2, 8, 2, 8, 5, 8, 2, 8, 5, 8, 6, 8, 6, 8, 6, 8, 6, 8, 9, 8, 9, 8, 9, 8, 9, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 9, 8, 9, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4

Offset: 1

Omar E. Pol, Oct 22 2011

Next term which is different from earlier in A195141.

			Since sqrt(2) = 1.414213562373095048801688724209698... the decimal expansion of square root of 2 starts with 1 (see A000796) hence the first leader in the race of digits is 1, so a(1) = 1. After 34 stages the new leader is 8 because the number 8 appears five times and the earlier leader appears four times, so a(2) = 8.

Cf. A002193, A195141, A195835, A195844, A195845, A195847.

More terms from D. S. McNeil, Oct 22 2011

A342325 a(n) is the position in digits of Pi where k(n) is for the first time leader in the race of digits of Pi. k(n) = 0, 1, ..., 9, 00, 01, ..., 99, 000, 001, ...

Original entry on oeis.org

174999, 4, 187, 1, 274, 11, 990213634, 320741, 108, 59, 16972551346, 98100646316

Offset: 0

Ruediger Jehn and Kester Habermann, Mar 08 2021

48 out of all 100 two-digit combinations are never in the lead when the first 100 billion digits of Pi are analyzed. 02 is the first of these 48, hence a(12) is unknown so far. The results for the 52 two-digit numbers which took the lead at some time are given in the link below.

			a(1) = 4 because the 1 becomes the leader in the race of digits of Pi for the first time after 4 digits: 3141.
a(41) = 2 because k(41) = 31 and 31 is the leader after two digits of Pi.

Ruediger Jehn, Leaderboard considering the first 100 billion digits

Cf. A000796, A195835.

A341430 Leaders in the race of digits of Catalan's constant.

Original entry on oeis.org

0, 9, 5, 9, 5, 1, 9, 1, 7, 9, 7, 0, 7, 9, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 6, 9, 6, 9, 8, 9, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9

Offset: 1

Omar E. Pol, Feb 11 2021

Next term which is different from earlier in A341438.

			The decimal expansion of Catalan's constant = 0.9159655941772190150546... starts with 0 (see A006752) hence the first leader in the race of digits is 0, so a(1) = 0.
After five stages the new leader is 9 because the number 9 appears twice and the earlier leader appears once, so a(2) = 9.
After eight stages the new leader is 5 because the number 5 appears three times and the earlier leader appears twice, so a(3) = 5.

Max Z. Scialabba, Table of n, a(n) for n = 1..1150
Seungmin Kim, World Record Computation of Catalan's Constant (600,000,000,100 Digits)

Cf. A006752, A195835, A195844, A195845, A195846, A195847, A341438.

More terms from Seungmin Kim added by Max Z. Scialabba, Dec 20 2023

A361434 Positions in Pi where the leader in the race of digits changes.

Original entry on oeis.org

1, 4, 11, 18, 59, 108, 187, 198, 274, 335, 338, 374, 381, 387, 433, 815, 848, 1495, 1629, 2002, 3554, 3565, 4112, 4318, 4569, 4592, 4613, 4618, 4643, 4727, 4733, 6103, 6118, 7074, 7153, 7319, 7521, 7562, 7567, 7684, 7748, 7757, 7764, 7989, 8205, 8561, 8620

Offset: 1

Alois P. Heinz, Mar 11 2023

			(3).14(1)592653(5)897932(3)8462643383279502884197169399375105820974(9)4...
New leaders are marked (). 3 is the leader from position 1 to 3 in Pi and later from position 18 to 58.  At position 4 the new leader (with 2 appearances) is 1.  At position 59 3 is displaced by 9.

Alois P. Heinz, Table of n, a(n) for n = 1..326

Subsequence of A361131.

Cf. A000796, A096567, A195835, A342325.

cp's OEIS Frontend

A195844 Leaders in the race of digits of e.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A195847 Leaders in the race of digits of Euler's constant (or Euler-Mascheroni constant) gamma.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A195845 Leaders in the race of digits of golden ratio phi.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A195846 Leaders in the race of digits of square root of 2.

Views

Author

Keywords

Comments

Examples

Crossrefs

Extensions

A342325 a(n) is the position in digits of Pi where k(n) is for the first time leader in the race of digits of Pi. k(n) = 0, 1, ..., 9, 00, 01, ..., 99, 000, 001, ...

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A341430 Leaders in the race of digits of Catalan's constant.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A361434 Positions in Pi where the leader in the race of digits changes.

Views

Author

Keywords

Examples

Links

Crossrefs