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

%I #9 Jun 11 2024 01:44:38

%S 11,15,34,35,47,59,103,110,115,122,123,142,146,154,159,167,179,195,

%T 203,207,214,239,247,251,262,287,290,311,318,319,323,339,354,355,362,

%U 394,434,447,466,538,542,563,599,627,682,707,718,739,743,759,774,782,867

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

%C Somu and Tran (2024) conjectured that there are finitely many such integers. It was also conjectured that 4005819 is the largest such integer. This conjecture was checked up to 10^8.

%H Duc Van Khanh Tran, <a href="/A373610/b373610.txt">Table of n, a(n) for n = 1..414</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. A000567, A005153.

%K nonn,hard

%O 1,1

%A _Duc Van Khanh Tran_, Jun 10 2024