Convergent series of integers with missing digits

被引：2

作者：

Nathanson, Melvyn B. ^{[1
]}

机构：

[1] CUNY, Lehman Coll, Bronx, NY 10468 USA

来源：

RAMANUJAN JOURNAL | 2022年 / 58卷 / 02期

关键词：

Integers with missing digits; Harmonic series; SUBSUMS;

D O I：

10.1007/s11139-021-00444-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A classical theorem of Kempner states that the sum of the reciprocals of positive integers with missing decimal digits converges. This result is extended to much larger families of "missing digits" sets of positive integers with convergent harmonic series.

引用

页码：667 / 676

页数：10

共 50 条

[21] SOME REMARKS CONCERNING THE SUM OF DIGITS OF INTEGERS
DRINGO, L
KATAI, I
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1981, 37 (1-3): : 165 - 172
[22] DECIMAL EXPANSIONS WITH MISSING DIGITS
STEEN, LA
JUST, E
AMERICAN MATHEMATICAL MONTHLY, 1967, 74 (07): : 865 - &
[23] Sets of integers with missing differences
Gupta, S
JOURNAL OF COMBINATORIAL THEORY SERIES A, 2000, 89 (01) : 55 - 69
[24] LINEAR-EQUATIONS IN INTEGERS WITH BOUNDED SUM OF DIGITS
SCHLICKEWEI, HP
JOURNAL OF NUMBER THEORY, 1990, 35 (03) : 335 - 344
[25] Sequences of integers with missing quotients
Chen, Yong-Gao
Yang, Hong-Xia
DISCRETE MATHEMATICS, 2010, 310 (05) : 1105 - 1111
[26] Distribution of digits in integers: fractal dimensions and zeta functions
Olsen, L
ACTA ARITHMETICA, 2002, 105 (03) : 253 - 277
[27] On the Distribution in Residue Classes of Integers with a Fixed Sum of Digits
Christian Mauduit
Carl Pomerance
András Sárközy
The Ramanujan Journal, 2005, 9 : 45 - 62
[28] SETS OF INTEGERS WITH MISSING DIFFERENCES
HARALAMBIS, NM
JOURNAL OF COMBINATORIAL THEORY SERIES A, 1977, 23 (01) : 22 - 33
[29] Representation of numbers with negative digits and multiplication of small integers
Puchta, JC
FIBONACCI QUARTERLY, 2002, 40 (01): : 66 - 67
[30] On the distribution in residue classes of integers with a fixed sum of digits
Mauduit, C
Pomerance, C
Sárközy, A
RAMANUJAN JOURNAL, 2005, 9 (1-2): : 45 - 62

← 1 2 3 4 5 →