A144812 -id:A144812 - cp's OEIS frontend

A144809 Decimal expansion of the constant 3.39277252592669675143137... arising in A144785.

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

Offset: 1

Artur Jasinski, Sep 21 2008

Cf. A076393, A144785, A144802, A144803, A144804, A144805, A144806, A144807, A144808, A144810, A144811, A144812.

A144801 Integers having ideal digital mean up to base 6.

Original entry on oeis.org

36990, 37230, 38670, 43350, 45390, 14492490, 14496810, 14512170, 14578050, 14579970, 14630970, 14655810, 14663730, 14685690, 14733810, 14741790, 14753010, 14758350, 14761350, 14779230, 14779710, 14780310, 14784090, 14801490, 14807190, 14807430, 14818650

Offset: 1

Reikku Kulon, Sep 21 2008

Subset of A031443, A144798, A144799 and A144800.

These numbers have digital mean dm(b, n) = (Sum_{i=1..d} 2*d_i - (b-1)) / (2*d) = 0, where d is the number of digits in the base b representation of n and d_i the individual digits, for 2 <= b <= 6.

Jason Yuen, Table of n, a(n) for n = 1..10000 (first 793 terms from Pontus von Brömssen)

Cf. A007953, A008591, A031443, A144777, A144798, A144799, A144800, A144812, A364714.

is(k,b) = my(d=digits(k,b)); vecsum(d)/#d == (b-1)/2;
isok(k) = is(k,2) && is(k,3) && is(k,4) && is(k,5) && is(k,6); \\ Michel Marcus, Aug 03 2023

Accidentally omitted terms added by Reikku Kulon, Sep 24 2008

a(24)-a(27) from Pontus von Brömssen, Aug 02 2023

A364714 Least positive integer whose average digit in base b equals (b-1)/2 (the expected value for random digits) for 2 <= b <= n.

Original entry on oeis.org

2, 38, 141, 3468, 36990, 36990

Offset: 2

Pontus von Brömssen, Aug 04 2023

a(n) has an even number of digits in all even bases b <= n.
a(8) <= 795482814912042180, a(9) and a(10) <= 836119295625913740. - Giorgos Kalogeropoulos, Aug 09 2023
a(8) and a(9) <= 789730327537467540, a(10) <= 789731071815355740, a(11) <= 789731549802436500. - Jason Yuen, May 17 2024
a(8) > A144812(10000) = 16960567248690 (last term in b-file for A144812). - Pontus von Brömssen, May 19 2024

			For n = 4, 141 is 10001101 in binary with average digit 1/2, 12020 in base 3 with average digit 2/2 = 1, and 2031 in base 4 with average digit 3/2. No smaller number has this property, so a(4) = 141.

a(2)-a(7) are the first terms of A031443, A144798, A144799, A144800, A144801, and A144812, respectively.

isokb(k, b) = my(d=digits(k,b)); vecsum(d)/#d == (b-1)/2;
isok(k, n) = for (b=2, n, if (!isokb(k, b), return(0));); 1;
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Aug 05 2023

cp's OEIS Frontend

A144809 Decimal expansion of the constant 3.39277252592669675143137... arising in A144785.

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A144801 Integers having ideal digital mean up to base 6.

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A364714 Least positive integer whose average digit in base b equals (b-1)/2 (the expected value for random digits) for 2 <= b <= n.

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