A074709 -id:A074709 - cp's OEIS frontend

A073761 Primitive numbers whose decimal expansion of 1/n is equidistributed in base 10.

61, 131, 181, 461, 491, 541, 571, 701, 811, 821, 941, 971, 1021, 1051, 1091, 1171, 1181, 1291, 1301, 1349, 1381, 1531, 1571, 1621, 1741, 1811, 1829, 1861, 2141, 2221, 2251, 2341, 2371, 2411, 2621, 2731, 2741, 2851, 2861, 2971, 3011, 3221, 3251, 3301

Offset: 1

Donald S. McDonald, Sep 02 2002

Usually once a number has the desired property, so do all its multiples. However there are exceptions. 61*7 in base 10 is not equidistributed. Multiples of earlier numbers are not included here.
From Jianing Song, Jul 29 2022: (Start)
There are 58 composite terms below 100000, 2 among which being even: a(239) = 25064 = 2^3 * 13 * 241, and a(613) = 72728 = 2^3 * 9091.
Conjecture 1: let p be a prime such that ord(10,p) is a multiple of 10, where ord(a,m) denotes the multiplicative order of a modulo m. Then p is a term if and only if 10 is a primitive root modulo p.
Conjecture 2: suppose that m is a term with bigomega(m) = 2, then m = p*q, where p == 1 (mod 10), q == 9 (mod 10), gcd(p-1,q-1) = 2, ord(10,p) = (p-1)/2, and ord(10,q) = q-1. Note that the converse is not true, though.
There are no counterexamples to the conjectures above below 100000.
Is there any odd term m such that bigomega(m) > 2? (End)

			61 is a term because 1/61 = .016393... (period 60 digits, 6 of each 0,1,..9).

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, revised edition, London, England, 1997, entry 61, page 110.

Jianing Song, Table of n, a(n) for n = 1..808 (all terms <= 100000)

Cf. A074709.

a = {}; Do[d = RealDigits[1/n][[1, 1]]; If[ !IntegerQ[d] && Count[d, 0] == Count[d, 1] == Count[d, 2] == Count[d, 3] == Count[d, 4] == Count[d, 5] == Count[d, 6] == Count[d, 7] == Count[d, 8] == Count[d, 9], If[ Select[n/a, IntegerQ] == {}, a = Append[a, n]]], {n, 11, 3330}]; a

Edited by Robert G. Wilson v, Sep 06 2002

A074900 Base 4 expansion of 1/n has equal percentage of each digit 0,1,2,3 (primitive values of n only).

Original entry on oeis.org

34, 194, 866, 1889, 2017, 2434, 2722, 2897, 4993, 7393, 7394, 7841, 10562, 10882, 11777, 11969, 15074, 16993, 17282, 20129, 20417, 20849, 23041, 24322, 35426, 40193, 40289, 44962, 49567, 55793, 59009, 59522, 63865, 64481, 65195, 85289, 86657, 87649, 103649

Offset: 1

Robert G. Wilson v, Sep 06 2002

Primitive means that if n is present then k*n is not for k >= 2.

Cf. A074709.

Data corrected and extended by Sean A. Irvine, Feb 01 2025

cp's OEIS Frontend

A073761 Primitive numbers whose decimal expansion of 1/n is equidistributed in base 10.

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