A373646 Positive integers that cannot be written as a sum of a practical number and an 18-gonal number.

10, 11, 14, 15, 23, 27, 35, 39, 44, 45, 47, 51, 62, 68, 70, 76, 77, 86, 92, 94, 95, 103, 110, 119, 125, 134, 137, 143, 149, 152, 153, 165, 170, 175, 182, 187, 202, 203, 206, 215, 223, 230, 233, 236, 239, 263, 283, 284, 287, 299, 314, 317, 319, 329, 332, 335

Offset

1,1

Comments

Somu and Tran (2024) conjectured that there are finitely many such integers. It was also conjectured that 8541224 is the largest such integer. This conjecture was checked up to 10^8.

Links

Duc Van Khanh Tran, Table of n, a(n) for n = 1..1020

Sai Teja Somu and Duc Van Khanh Tran, On sums of practical numbers and polygonal numbers, Journal of Integer Sequences, 27(5), 2024.

Crossrefs

Cf. A005153, A051870.

Sequence in context: A373634 A373633 A373665 * A335237 A214864 A062844

Adjacent sequences: A373642 A373644 A373645 * A373647 A373648 A373649

Keyword

nonn,hard

Author

Duc Van Khanh Tran, Jun 12 2024

Status

approved