A195844 -id:A195844 - cp's OEIS frontend

A195138 First digit to appear n times in the decimal expansion of e.

2, 2, 8, 8, 2, 2, 2, 2, 9, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 3, 9, 9, 2, 7, 4, 4, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9

Offset: 1

Omar E. Pol, Oct 22 2011

The digits 0 and 5 do not appear among the first 30000 terms. When do they first appear? - Jianing Song, Apr 01 2021

			From _Michael De Vlieger_, Sep 10 2017: (Start)
a(n) is the first decimal digit of e that first appears n times when e is expanded to the -m place:
   n  a(n)  m
   1   2    0
   2   2    4
   3   8    7
   4   8    9
   5   2   22
   6   2   30
   7   2   33
   8   2   40
   9   9   58
  10   7   63
  11   7   64
  12   7   68
  13   7   78
  14   7   83
  15   7   89
  16   7   99
(End)

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Cf. A001113, A195844, A277270, A290643, A290644.

Cf. A096567, A195139, A195141, A280811, A341438.

With[{e = First@ RealDigits[N[E, 10^4]]}, Function[t, -1 + Map[FirstPosition[t, #] &, Range@ Max@ t][[All, -1]]]@ Table[BinCounts[Take[e, n], {0, 10, 1}], {n, 10^3}]] (* Michael De Vlieger, Sep 10 2017 *)

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

A195835 Leaders in the race of digits of Pi.

Original entry on oeis.org

3, 1, 5, 3, 9, 8, 2, 8, 4, 8, 2, 8, 2, 4, 1, 9, 1, 9, 1, 9, 1, 9, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 1, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 1, 4

Offset: 1

Omar E. Pol, Oct 22 2011

Next term which is different from earlier in A096567.
The number 4 wins 71.7% of the first 100 million races (occurs most often in 71.7% of the races). It is also the leader after 100 million digits with a comfortable lead (10,003,863 occurrences compared to 10,002,475 occurrences of the 1 that was winning 15.9% of the first 100 million races). All numbers except the 6 were in the lead at some time. Number 6 was almost in the lead after 48,500 digits, only two occurrences short of the 1 at that time. In the first 100,000,000 digits of Pi the number 6 appears about 4450 times less than the current leader 4. But as the next comment shows the 6 finally takes the lead after 990,213,634 digits. - Ruediger Jehn, Jan 27 2021
Position at which a number (0 to 9) is leader for the first time: 174999, 4, 187, 1, 274, 11, 990213634, 320741, 108, 59 (see A342325). - Kester Habermann, Jan 27 2021

			The decimal expansion of Pi = 3.1415926535... starts with 3 (see A000796) hence the first leader in the race of digits is 3, so a(1) = 3. After 4 stages the new leader is 1 because the number 1 appears twice and the earlier leader appears once, so a(2) = 1. After 11 stages the new leader is 5 because the number 5 appears three times and the earlier leader appears twice, so a(3) = 5.

Ruediger Jehn, Table of n, a(n) for n = 1..3845

Cf. A000796, A096567, A195844, A195845, A195846, A195847, A342325.

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

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

cp's OEIS Frontend

A195138 First digit to appear n times in the decimal expansion of e.

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A195835 Leaders in the race of digits of Pi.

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

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

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

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

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