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Positive integers that cannot be written as a sum of a practical number and a decagonal number.
1

%I #7 Jun 11 2024 01:44:42

%S 10,15,23,27,44,62,71,77,95,102,119,137,143,188,194,242,249,269,278,

%T 284,311,323,338,359,413,422,509,519,524,593,599,614,656,662,663,683,

%U 698,779,824,944,974,1028,1049,1058,1061,1073,1124,1139,1178,1208,1293,1304

%N Positive integers that cannot be written as a sum of a practical number and a decagonal number.

%C Somu and Tran (2024) conjectured that there are finitely many such integers. It was also conjectured that 13613213 is the largest such integer. This conjecture was checked up to 10^8.

%H Duc Van Khanh Tran, <a href="/A373613/b373613.txt">Table of n, a(n) for n = 1..341</a>

%H Sai Teja Somu and Duc Van Khanh Tran, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Somu/somu5.html">On sums of practical numbers and polygonal numbers</a>, Journal of Integer Sequences, 27(5), 2024.

%Y Cf. A001107, A005153.

%K nonn,hard

%O 1,1

%A _Duc Van Khanh Tran_, Jun 10 2024