A374344 a(n) is the number of ways n can be written as a sum of a practical number and two heptagonal numbers.

1, 2, 2, 2, 1, 2, 1, 3, 3, 2, 1, 2, 2, 2, 2, 3, 1, 3, 3, 6, 2, 3, 2, 3, 3, 5, 3, 2, 2, 4, 4, 4, 2, 3, 3, 5, 6, 6, 3, 4, 3, 7, 6, 4, 2, 3, 4, 4, 5, 5, 2, 2, 4, 6, 5, 7, 5, 5, 4, 5, 6, 5, 4, 7, 4, 6, 6, 7, 2, 5, 4, 7, 6, 9, 4, 5, 3, 5, 6, 8

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. A000566, A005153.

Sequence in context: A339812 A238568 A368148 * A238421 A105154 A076447

Adjacent sequences: A374341 A374342 A374343 * A374345 A374346 A374347

Keyword

nonn

Author

Duc Van Khanh Tran, Jul 08 2024

Status

approved