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A373616
Positive integers that cannot be written as a sum of a practical number and a 13-gonal number.
1
10, 11, 22, 23, 26, 27, 34, 35, 39, 46, 47, 50, 51, 58, 59, 62, 63, 70, 75, 83, 87, 95, 99, 107, 111, 115, 122, 137, 138, 146, 149, 152, 159, 165, 167, 184, 185, 188, 194, 206, 218, 222, 245, 248, 263, 282, 284, 287, 314, 329, 345, 354, 357, 359, 362, 383, 386
OFFSET
1,1
COMMENTS
Somu and Tran (2024) conjectured that there are finitely many such integers. It was also conjectured that 1612172 is the largest such integer. This conjecture was checked up to 10^8.
LINKS
Sai Teja Somu and Duc Van Khanh Tran, On sums of practical numbers and polygonal numbers, Journal of Integer Sequences, 27(5), 2024.
EXAMPLE
11 is in the sequence as 13-gonal numbers below 11 are 0, 1 and both 11-0 and 11-1 are not practical. - David A. Corneth, Jun 11 2024
CROSSREFS
Sequence in context: A041200 A041847 A113702 * A102488 A022315 A061590
KEYWORD
nonn,hard
AUTHOR
Duc Van Khanh Tran, Jun 11 2024
STATUS
approved