A374415 a(n) is the number of ways n can be written as a sum of a practical number and two octagonal numbers.

1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 2, 2, 2, 1, 2, 3, 3, 1, 4, 2, 3, 2, 4, 3, 3, 2, 4, 3, 4, 2, 4, 4, 3, 1, 3, 4, 3, 2, 4, 5, 5, 3, 5, 4, 4, 2, 5, 6, 5, 2, 4, 3, 4, 1, 6, 5, 5, 2, 4, 4, 5, 3, 6, 5, 5, 4, 5, 6, 5, 3, 7, 5, 5, 3, 4, 6, 5, 3, 6

Offset

1,2

Comments

Somu and Tran (2024) proved that a(n) > 0 for sufficiently large n and conjectured that a(n) > 0 for all n > 0. The conjecture was checked up to 10^8.

Links

Duc Van Khanh Tran, Table of n, a(n) for n = 1..10000

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. A000567, A005153.

Sequence in context: A080354 A374416 A238529 * A195150 A022307 A029413

Adjacent sequences: A374412 A374413 A374414 * A374416 A374417 A374418

Keyword

nonn

Author

Duc Van Khanh Tran, Jul 08 2024

Status

approved